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photo of Markus Linckelmann

Professor Markus Linckelmann

Professor of Mathematics

School of Science and TechnologyDepartment of Mathematics

Contact details

  • +44 (0)20 7040 8459
  • markus.linckelmann.1@city.ac.uk

Address

Professor Markus Linckelmann E229, Drysdale Building
City, University of London
Northampton Square
London EC1V 0HB
United Kingdom
  • About
  • Research
  • Publications

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

  1. Habilitation à diriger des recherches Mathematics, University of Paris 7 CNRS, France, 1996
  2. PhD Mathematics, University of Paris 7 CNRS, France, 1988
  3. Dipl. Math. Mathematics and Computer Science, Technical University Munich, Germany, 1985

Employment

  1. Professor, City, University of London, Sep 2012 – present
  2. Invited Researcher, Mathematical Sciences Research Institute, Jan – May 2008
  3. 6th Century Professor, University of Aberdeen, Sep 2005 – Aug 2012
  4. Visiting Research Fellow, École Polytechnique Fédérale de Lausanne, Mar – Jun 2005
  5. Associate Professor, Ohio State University, Sep 2002 – Aug 2005
  6. Visiting Professor, University of Minnesota, Sep – Dec 1998
  7. Visiting Research Fellow, University of Stuttgart, May – Nov 1995
  8. Visiting Professor, University of Minnesota, Sep – Dec 1994
  9. Visiting Professor, Middle East Technical University, Sep 1992 – Jun 1993
  10. Invited Researcher, Mathematical Sciences Research Institute, Oct – Dec 1990
  11. Chargé de Recherche, Centre National de la Recherche Scientifique (CNRS), Oct 1988 – Aug 2002

Research

1st supervisor

  • William Murphy, Research Student

Publications

Publications by category

Chapter

  • Linckelmann, M. (2018). Finite-dimensional algebras arising as blocks
    of finite group algebras.
    (pp. 155–188). American Mathematical
    Society.

Conference papers and proceedings (3)

  • Linckelmann, M. (2018). On Automorphisms and Focal Subgroups of Blocks.
  • Kessar, R. and Linckelmann, M. (2018). Descent of Equivalences and Character Bijections.
  • Linckelmann, M. (2011). Cohomology of block algebras of finite groups.

Journal articles (88)

  • 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 of the American Mathematical Society, 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.
  • 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.

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