Contact details
About
Overview
Professor Linckelmann received a Diploma in Mathematics from the Technical University in Munich (1985), followed by a PhD in Mathematics from the University Paris VII (1988). He joined the French National Scientific Foundation CNRS as a researcher, before moving to The Ohio State University in Columbus, USA, as Associate Professor in 2002. He moved to the University of Aberdeen for a Sixth Century Professorship in 2005, and joined City, University of London in 2012.
Qualifications
- Habilitation à diriger des recherches Mathematics, University of Paris 7 CNRS, France, 1996
- PhD Mathematics, University of Paris 7 CNRS, France, 1988
- Dipl. Math. Mathematics and Computer Science, Technical University Munich, Germany, 1985
Employment
- Professor, City, University of London, United Kingdom, September 2012 - present
- Invited Researcher, Mathematical Sciences Research Institute, United States, January - May 2008
- 6th Century Professor, University of Aberdeen, United Kingdom, September 2005 - August 2012
- Visiting Research Fellow, École Polytechnique Fédérale de Lausanne, Switzerland, March - June 2005
- Associate Professor, Ohio State University, United States, September 2002 - August 2005
- Visiting Professor, University of Minnesota, United States, September - December 1998
- Visiting Research Fellow, University of Stuttgart, Germany, May - November 1995
- Visiting Professor, University of Minnesota, United States, September - December 1994
- Visiting Professor, Middle East Technical University, Turkey, September 1992 - June 1993
- Invited Researcher, Mathematical Sciences Research Institute, United States, October - December 1990
- Chargé de Recherche, Centre National de la Recherche Scientifique (CNRS), France, October 1988 - August 2002
Research students
1stsupervisor
- William Murphy, Research Student
Publications
Publications by category
Books (2)
- Linckelmann, M. (2018). The Block Theory of Finite Group Algebras. Cambridge University Press. ISBN 9781108425919.
- Linckelmann, M. (2018). The Block Theory of Finite Group Algebras. Cambridge University Press.
Chapter
- Linckelmann, M. (2018). Finite-dimensional algebras arising as blocks of finite group algebras. (pp. 155-188). American Mathematical Society. ISBN 9781470435769.
Conference papers and proceedings (3)
- Linckelmann, M. On Automorphisms and Focal Subgroups of Blocks. .doi:10.1007/978-3-319-94033-5_9
- Kessar, R. and Linckelmann, M. Descent of Equivalences and Character Bijections. .doi:10.1007/978-3-319-94033-5_7
- Linckelmann, M. Cohomology of block algebras of finite groups. .
Journal articles (97)
- KESSAR, R., LINCKELMANN, M., LYND, J. and SEMERARO, J. (2026). WEIGHT CONJECTURES FOR FUSION SYSTEMS ON AN EXTRASPECIAL GROUP. Journal of the Australian Mathematical Society, 120(3), pp. 373-393. doi:10.1017/s1446788725101390
- Linckelmann, M. and Wang, J. (2025). On the solvability of the Lie algebra HH1(B)$\mathrm{HH}^1(B)$ for blocks of finite groups. Journal of the London Mathematical Society, 112(6). doi:10.1112/jlms.70407
- Linckelmann, M. (2025). The operad of Latin hypercubes. Glasgow Mathematical Journal, 67(3), pp. 475-486. doi:10.1017/s0017089525000047
- Linckelmann, M. (2025). Tate duality and transfer for symmetric algebras over complete discrete valuation rings. Proceedings of the Edinburgh Mathematical Society, 68(3), pp. 763-786. doi:10.1017/s0013091524000671
- Linckelmann, M. (2024). Inverse images of block varieties. Communications in Algebra, 52(5), pp. 2086-2100. doi:10.1080/00927872.2023.2281600
- Linckelmann, M. (2023). On abelian subcategories of triangulated categories. Mathematische Zeitschrift, 306. doi:10.1007/s00209-023-03396-2
- Benson, D., Kessar, R. and Linckelmann, M. (2023). Hochschild cohomology of symmetric groups and generating functions, II. Research in the Mathematical Sciences, 10(2). doi:10.1007/s40687-023-00382-2
- Benson, D., Kessar, R. and Linckelmann, M. (2023). Hochschild cohomology of symmetric groups and generating functions. Journal of Group Theory, 0(0). doi:10.1515/jgth-2022-0130
- Benson, D., Kessar, R. and Linckelmann, M. (2023). Structure of blocks with normal defect and abelian inertial quotient. Forum of Mathematics, Sigma, 11. doi:10.1017/fms.2023.13
- Kessar, R. and Linckelmann, M. (2021). A block theoretic proof of Thompson’s $$A\times B$$-lemma. Archiv der Mathematik, 117(5), pp. 481-483. doi:10.1007/s00013-021-01638-5
- Benson, D., Kessar, R. and Linckelmann, M. (2021). On the BV structure of the Hochschild cohomology of finite group algebras. Pacific Journal of Mathematics, 313(1), pp. 1-44. doi:10.2140/pjm.2021.313.1
- Linckelmann, M. and Murphy, W. (2021). A Nine-Dimensional Algebra which is not a Block of a Finite Group. The Quarterly Journal of Mathematics, 72(3), pp. 1077-1088. doi:10.1093/qmath/haaa061
- Linckelmann, M. (2020). A note on vertices of indecomposable tensor products. Journal of Group Theory, 23(3), pp. 385-391. doi:10.1515/jgth-2019-0130
- Linckelmann, M. and Rubio y Degrassi, L. (2020). On the Lie algebra structure of 𝐻𝐻¹(𝐴) of a finite-dimensional algebra 𝐴. Proceedings of the American Mathematical Society, 148(5), pp. 1879-1890. doi:10.1090/proc/14875
- Benson, D., Kessar, R. and Linckelmann, M. (2019). BLOCKS WITH NORMAL ABELIAN DEFECT AND ABELIAN p′ INERTIAL QUOTIENT. The Quarterly Journal of Mathematics, 70(4), pp. 1437-1448. doi:10.1093/qmathj/haz025
- Kessar, R., Linckelmann, M., Lynd, J. and Semeraro, J. (2019). Weight conjectures for fusion systems. Advances in Mathematics, 357, pp. 106825-106825. doi:10.1016/j.aim.2019.106825
- Linckelmann, M. (2019). The strong Frobenius numbers for cyclic defect blocks are equal to one. Communications in Algebra pp. 1-8. doi:10.1080/00927872.2019.1635139
- Linckelmann, M., Boltje, R. and Kessar, R. (2019). On Picard groups of blocks of finite groups. Journal of Algebra. doi:10.1016/j.jalgebra.2019.02.045
- Kessar, R. and Linckelmann, M. (2019). Dade’s ordinary conjecture implies the Alperin–McKay conjecture. Archiv der Mathematik, 112(1), pp. 19-25. doi:10.1007/s00013-018-1230-9
- Linckelmann, M. (2018). The dominant dimension of cohomological Mackey functors. Journal of Algebra and Its Applications, 17(12), pp. 1850228-1850228. doi:10.1142/s0219498818502286
- Linckelmann, M. (2018). A NOTE ON THE DEPTH OF A SOURCE ALGEBRA OVER ITS DEFECT GROUP. International Electronic Journal of Algebra pp. 68-68. doi:10.24330/ieja.440216
- Linckelmann, M. and Rognerud, B. (2018). On Morita and derived equivalences for cohomological Mackey algebras. Mathematische Zeitschrift, 289(1-2), pp. 39-50. doi:10.1007/s00209-017-1942-8
- Linckelmann, M. (2018). Integrable derivations and stable equivalences of Morita type. Proceedings of the Edinburgh Mathematical Society, 61(2), pp. 343-362. doi:10.1017/S0013091517000098
- Linckelmann, M. and Rubio Y Degrassi, L. (2018). Block algebras with HH1 a simple Lie algebra. The Quarterly Journal of Mathematics. doi:10.1093/qmath/hay017
- Linckelmann, M. (2017). Quillen’s stratification for fusion systems. Communications in Algebra, 45(12), pp. 5227-5229. doi:10.1080/00927872.2017.1301461
- Benson, D., Kessar, R. and Linckelmann, M. (2017). On blocks of defect two and one simple module, and Lie algebra structure of HH1. Journal of Pure and Applied Algebra, 221(12), pp. 2953-2973. doi:10.1016/j.jpaa.2017.02.010
- Eisele, F., Geline, M., Kessar, R. and Linckelmann, M. (2017). On tate duality and a projective scalar property for symmetric algebras. Pacific Journal of Mathematics, 293(2), pp. 277-300. doi:10.2140/pjm.2018.293.277
- Kessar, R., Külshammer, B. and Linckelmann, M. (2017). Anchors of irreducible characters. Journal of Algebra, 475, pp. 113-132. doi:10.1016/j.jalgebra.2015.11.034
- Linckelmann, M. (2016). On equivalences for cohomological Mackey functors. Representation Theory, 20(7), pp. 162-171. doi:10.1090/ert/482
- Kessar, R., Koshitani, S. and Linckelmann, M. (2015). On symmetric quotients of symmetric algebras. Journal of Algebra, 442, pp. 423-437. doi:10.1016/j.jalgebra.2014.05.035
- Kessar, R., Koshitani, S. and Linckelmann, M. (2015). On symmetric quotients of symmetric algebras. Journal of Algebra, 442, pp. 423-437. doi:10.1016/j.jalgebra.2014.05.035
- Kessar, R., Koshitani, S. and Linckelmann, M. (2015). ON THE BRAUER INDECOMPOSABILITY OF SCOTT MODULES. The Quarterly Journal of Mathematics, 66(3), pp. 895-903. doi:10.1093/qmath/hav010
- Linckelmann, M. (2015). On stable equivalences with endopermutation source. Journal of Algebra, 434, pp. 27-45. doi:10.1016/j.jalgebra.2015.03.014
- Kessar, R., Linckelmann, M. and Navarro, G. (2015). A characterisation of nilpotent blocks. Proceedings of the American Mathematical Society, 143(12), pp. 5129-5138. doi:10.1090/proc/12646
- Kessar, R. and Linckelmann, M. (2015). On the Castelnuovo-Mumford regularity of the cohomology of fusion systems and of the Hochschild cohomology of block algebras. Groups St. Andrews 2013, London Mathematical Society Lecture Note Series(422), pp. 324-330
- Linckelmann, M. (2014). A version of alperin's weight conjecture for finite category algebras. Journal of Algebra, 398, pp. 386-395. doi:10.1016/j.jalgebra.2013.02.010
- Linckelmann, M. (2013). Tate duality and transfer in hochschild cohomology. Journal of Pure and Applied Algebra, 217(12), pp. 2387-2399. doi:10.1016/j.jpaa.2013.04.004
- Linckelmann, M. (2013). ON INVERSE CATEGORIES AND TRANSFER IN COHOMOLOGY. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 56(1), pp. 187-210. doi:10.1017/S0013091512000211
- LINCKELMANN, M. and Stolorz, M. (2013). Quasi-hereditary twisted category algebras. Journal of Algebra, 385, pp. 1-13. doi:10.1016/j.jalgebra.2013.02.036
- Linckelmann, M. (2012). Tate duality and transfer in Hochschild cohomology.
- Kessar, R. and Linckelmann, M. (2012). On the Hilbert series of Hochschild cohomology of block algebras. Journal of Algebra, 371, pp. 457-461. doi:10.1016/j.jalgebra.2012.07.020
- Linckelmann, M. and Stolorz, M. (2012). On simple modules over twisted finite category algebras. Proceedings of the American Mathematical Society, 140(11), pp. 3725-3737. doi:10.1090/S0002-9939-2012-11381-4
- Kessar, R., Koshitani, S. and Linckelmann, M. (2012). Conjectures of Alperin and Broué for 2-blocks with elementary abelian defect groups of order 8. Journal für die reine und angewandte Mathematik (Crelles Journal), 2012(671), pp. 85-130. doi:10.1515/CRELLE.2011.162
- Kessar, R. and Linckelmann, M. (2011). Bounds for Hochschild cohomology of block algebras. Journal of Algebra, 337(1), pp. 318-322. doi:10.1016/j.jalgebra.2011.03.009
- Craven, D.A., Eaton, C.W., Kessar, R. and Linckelmann, M. (2011). The structure of blocks with a Klein four defect group. Mathematische Zeitschrift, 268(1-2), pp. 441-476. doi:10.1007/s00209-010-0679-4
- Linckelmann, M. (2011). Finite generation of Hochschild cohomology of Hecke algebras of finite classical type in characteristic zero. Bulletin of the London Mathematical Society, 43(5), pp. 871-885. doi:10.1112/blms/bdr024
- Kessar, R. and Linckelmann, M. (2010). The graded center of the stable category of a Brauer tree algebra. Quarterly Journal of Mathematics, 61(3), pp. 337-349. doi:10.1093/qmath/han038
- Linckelmann, M. and Stancu, R. (2010). On the graded center of the stable category of a finite p-group. Journal of Pure and Applied Algebra, 214(6), pp. 950-959. doi:10.1016/j.jpaa.2009.09.004
- Kessar, R. and Linckelmann, M. (2010). On stable equivalences and blocks with one simple module. Journal of Algebra, 323(6), pp. 1607-1621. doi:10.1016/j.jalgebra.2010.01.006
- Linckelmann, M. (2010). Hochschild and block cohomology varieties are isomorphic. Journal of the London Mathematical Society, 81(2), pp. 389-411. doi:10.1112/jlms/jdp078
- Linckelmann, M. (2009). On graded centres and block cohomology. Proceedings of the Edinburgh Mathematical Society, 52(2), pp. 489-514. doi:10.1017/S0013091507001137
- Linckelmann, M. (2009). On dimensions of block algebras. Mathematical Research Letters, 16(6), pp. 1011-1014. doi:10.4310/MRL.2009.v16.n6.a9
- Linckelmann, M. (2009). On H* (C{script}; k×) for fusion systems. Homology Homotopy and Applications, 11(1), pp. 203-218. doi:10.4310/HHA.2009.v11.n1.a10
- Linckelmann, M. (2009). Trivial source bimodule rings for blocks and p-permutation equivalences. Transactions of the American Mathematical Society, 361(3), pp. 1279-1316. doi:10.1090/s0002-9947-08-04577-7
- Linckelmann, M. and Mazza, N. (2009). The Dade group of a fusion system. Journal of Group Theory, 12(1), pp. 55-74. doi:10.1515/JGT.2008.060
- Linckelmann, M. (2009). The orbit space of a fusion system is contractible. Proceedings of the London Mathematical Society, 98(1), pp. 191-216. doi:10.1112/plms/pdn029
- Kessar, R. and Linckelmann, M. (2009). On two theorems of Flavell. Archiv Der Mathematik, 92(1), pp. 1-6. doi:10.1007/s00013-008-2911-6
- Linckelmann, M. (2009). ON DIMENSIONS OF BLOCK ALGEBRAS. MATHEMATICAL RESEARCH LETTERS, 16(5-6), pp. 1011-1014. doi:10.4310/MRL.2009.v16.n6.a9
- Linckelmann, M. (2009). TRIVIAL SOURCE BIMODULE RINGS FOR BLOCKS AND p-PERMUTATION EQUIVALENCES. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 361(3), pp. 1279-1316
- Kessar, R. and Linckelmann, M. (2008). ZJ-theorems for fusion systems. Transactions of the American Mathematical Society, 360(6), pp. 3093-3106. doi:10.1090/S0002-9947-08-04275-X
- Linckelmann, M. (2007). Blocks of minimal dimension. Archiv Der Mathematik, 89(4), pp. 311-314. doi:10.1007/s00013-007-2242-z
- Holm, T., Kessar, R. and Linckelmann, M. (2007). Blocks with a quaternion defect group over a 2-adic ring: The case Ã4. Glasgow Mathematical Journal, 49(1), pp. 29-43. doi:10.1017/S0017089507003394
- Kessar, R. and Linckelmann, M. (2006). On blocks of strongly p-solvable groups. Archiv Der Mathematik, 87(6), pp. 481-487. doi:10.1007/s00013-006-1826-3
- Linckelmann, M. (2006). Simple fusion systems and the Solomon 2-local groups. Journal of Algebra, 296(2), pp. 385-401. doi:10.1016/j.jalgebra.2005.09.024
- Linckelmann, M. (2006). A note on the Schur multiplier of a fusion system. Journal of Algebra, 296(2), pp. 402-408. doi:10.1016/j.jalgebra.2005.03.039
- Linckelmann, M. and Schroll, S. (2005). A two-sided q-analogue of the Coxeter complex. Journal of Algebra, 289(1), pp. 128-134. doi:10.1016/j.jalgebra.2005.03.026
- Linckelmann, M. (2005). Alperin's weight conjecture in terms of equivariant Bredon cohomology. Mathematische Zeitschrift, 250(3), pp. 495-513. doi:10.1007/s00209-004-0753-x
- LINCKELMANN, M. and SCHROLL, S. (2005). ON THE COXETER COMPLEX AND ALVIS–CURTIS DUALITY FOR PRINCIPAL ℓ-BLOCKS OF GLn(q). Journal of Algebra and Its Applications, 04(03), pp. 225-229. doi:10.1142/s0219498805001198
- Benson, D.J. and Linckelmann, M. (2005). Vertex and source determine the block variety of an indecomposable module. Journal of Pure and Applied Algebra, 197(1-3), pp. 11-17. doi:10.1016/j.jpaa.2004.08.032
- Koshitani, S. and Linckelmann, M. (2005). The indecomposability of a certain bimodule given by the Brauer construction. Journal of Algebra, 285(2), pp. 726-729. doi:10.1016/j.jalgebra.2004.08.031
- Linckelmann, M. (2004). Fusion category algebras. Journal of Algebra, 277(1), pp. 222-235. doi:10.1016/j.jalgebra.2003.12.010
- Kessar, R. and Linckelmann, M. (2003). A block theoretic analogue of a theorem of Glauberman and Thompson. Proceedings of the American Mathematical Society, 131(1), pp. 35-40. doi:10.1090/S0002-9939-02-06506-1
- Kessar, R., Linckelmann, M. and Robinson, G.R. (2002). Local control in fusion systems of p-blocks of finite groups. Journal of Algebra, 257(2), pp. 393-413. doi:10.1016/S0021-8693(02)00517-3
- Linckelmann, M. (2002). Quillen stratification for block varieties. Journal of Pure and Applied Algebra, 172(2-3), pp. 257-270. doi:10.1016/S0022-4049(01)00143-8
- Linckelmann, M. and Stalder, B. (2002). A reciprocity for symmetric algebras. Quarterly Journal of Mathematics, 53(2), pp. 201-205. doi:10.1093/qjmath/53.2.201
- Linckelmann, M. (2002). Induction for interior algebras. Quarterly Journal of Mathematics, 53(2), pp. 195-200. doi:10.1093/qjmath/53.2.195
- Kessar, R. and Linckelmann, M. (2002). On blocks with frobenius inertial quotient. Journal of Algebra, 249(1), pp. 127-146. doi:10.1006/jabr.2001.9058
- Harris, M.E. and Linckelmann, M. (2002). On the Glauberman and Watanabe correspondences for blocks of finite p-solvable groups. Transactions of the American Mathematical Society, 354(9), pp. 3435-3453. doi:10.1090/S0002-9947-02-02990-2
- Kessar, R. and Linckelmann, M. (2002). On perfect isometries for tame blocks. Bulletin of the London Mathematical Society, 34(1), pp. 46-54. doi:10.1112/S0024609301008633
- Linckelmann, M. (2001). On splendid derived and stable equivalences between blocks of finite groups. Journal of Algebra, 242(2), pp. 819-843. doi:10.1006/jabr.2001.8812
- Alperin, J.L., Linckelmann, M. and Rouquier, R. (2001). Source algebras and source modules. Journal of Algebra, 239(1), pp. 262-271. doi:10.1006/jabr.2000.8625
- Linckelmann, M. (2000). On the Hochschild cohomology of commutative Hopf algebras. Archiv Der Mathematik, 75(6), pp. 410-412. doi:10.1007/s000130050523
- Harris, M.E. and Linckelmann, M. (2000). Splendid derived equivalences for blocks of finite p-solvable groups. Journal of the London Mathematical Society, 62(1), pp. 85-96. doi:10.1112/S0024610700008966
- Linckelmann, M. (1999). Varieties in block theory. Journal of Algebra, 215(2), pp. 460-480. doi:10.1006/jabr.1998.7724
- Linckelmann, M. (1999). Transfer in Hochschild Cohomology of Blocks of Finite Groups. Algebras and Representation Theory, 2(2), pp. 107-135. doi:10.1023/A:1009979222100
- Linckelmann, M. (1998). On derived equivalences and local structure of blocks of finite groups. Turkish Journal of Mathematics, 22(1), pp. 93-107
- Linckelmann, M. (1996). Stable equivalences of Morita type for self-injective algebras and p-groups. Mathematische Zeitschrift, 223(1), pp. 87-100. doi:10.1007/pl00004556
- Linckelmann, M. (1996). Stable equivalences of Morita type for self-injective algebras and p-groups. Mathematische Zeitschrift, 223(1), pp. 87-100. doi:10.1007/BF02621590
- Linckelmann, M. (1996). The isomorphism problem for cyclic blocks and their source algebras. Inventiones Mathematicae, 125(2), pp. 265-283. doi:10.1007/s002220050075
- Linckelmann, M. (1994). The source algebras of blocks with a klein four defect group. Journal of Algebra, 167(3), pp. 821-854. doi:10.1006/jabr.1994.1214
- Linckelmann, M. (1994). A derived equivalence for blocks with dihedral defect groups. Journal of Algebra, 164(1), pp. 244-255. doi:10.1006/jabr.1994.1061
- Linckelmann, M. (1991). Derived equivalence for cyclic blocks over a P-adic ring. Mathematische Zeitschrift, 207(1), pp. 293-304. doi:10.1007/BF02571389
- Linckelmann, M. (1989). Modules in the sources of Green's exact sequences for cyclic blocks. Inventiones Mathematicae, 97(1), pp. 129-140. doi:10.1007/BF01850657
- LINCKELMANN, M. (1988). THE CENTER OF A BLOCK WITH CYCLIC DEFECT-GROUPS. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 306(17), pp. 727-730
- LINCKELMANN, M. (1987). THE STABLE CATEGORY OF A SELF INJECTIVE ALGEBRA IS TRIANGULATED. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 305(10), pp. 403-406
- LINCKELMANN, M. (1987). THE COMMUTING ALGEBRA OF PROJECTIVE PERIODIC RESOLUTIONS. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 304(19), pp. 575-578
- LINCKELMANN, M. and PUIG, L. (1987). STRUCTURE OF PARA'-EXTENSIONS OF NILPOTENT BLOCKS. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 304(8), pp. 181-184