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Professor Markus Linckelmann

Professor of Mathematics

School of Mathematics, Computer Science and Engineering Department of Mathematics

Contact details

Address

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

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

Publications

Publications by category

Chapter

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

Conference papers and proceedings (3)

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

Journal articles (88)

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Linckelmann, M. (2017). Quillen’s stratification for fusion systems. Communications in Algebra, 45(12), pp. 5227–5229. doi:10.1080/00927872.2017.1301461.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. Linckelmann, M. (2015). On stable equivalences with endopermutation source. Journal of Algebra, 434, pp. 27–45. doi:10.1016/j.jalgebra.2015.03.014.
  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. 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.
  30. 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.
  31. Linckelmann, M. (2012). Tate duality and transfer in Hochschild cohomology. .
  32. 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.
  33. 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.
  34. 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.
  35. 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.
  36. 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.
  37. 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.
  38. 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.
  39. 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.
  40. 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.
  41. 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.
  42. Linckelmann, M. (2009). On graded centres and block cohomology. Proceedings of the Edinburgh Mathematical Society, 52(2), pp. 489–514. doi:10.1017/S0013091507001137.
  43. Linckelmann, M. (2009). On dimensions of block algebras. Mathematical Research Letters, 16(6), pp. 1011–1014. doi:10.4310/MRL.2009.v16.n6.a9.
  44. 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.
  45. 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.
  46. 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.
  47. 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.
  48. 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.
  49. Linckelmann, M. (2009). ON DIMENSIONS OF BLOCK ALGEBRAS. MATHEMATICAL RESEARCH LETTERS, 16(5-6), pp. 1011–1014.
  50. Linckelmann, M. (2009). TRIVIAL SOURCE BIMODULE RINGS FOR BLOCKS AND p-PERMUTATION EQUIVALENCES. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 361(3), pp. 1279–1316.
  51. 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.
  52. Linckelmann, M. (2007). Blocks of minimal dimension. Archiv der Mathematik, 89(4), pp. 311–314. doi:10.1007/s00013-007-2242-z.
  53. 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.
  54. 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.
  55. 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.
  56. 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.
  57. 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.
  58. 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.
  59. 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.
  60. 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.
  61. 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.
  62. Linckelmann, M. (2004). Fusion category algebras. Journal of Algebra, 277(1), pp. 222–235. doi:10.1016/j.jalgebra.2003.12.010.
  63. 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.
  64. 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.
  65. 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.
  66. 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.
  67. Linckelmann, M. (2002). Induction for interior algebras. Quarterly Journal of Mathematics, 53(2), pp. 195–200. doi:10.1093/qjmath/53.2.195.
  68. 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.
  69. 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.
  70. 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.
  71. 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.
  72. 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.
  73. Linckelmann, M. (2000). On the Hochschild cohomology of commutative Hopf algebras. Archiv der Mathematik, 75(6), pp. 410–412. doi:10.1007/s000130050523.
  74. 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.
  75. Linckelmann, M. (1999). Varieties in block theory. Journal of Algebra, 215(2), pp. 460–480. doi:10.1006/jabr.1998.7724.
  76. 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.
  77. Linckelmann, M. (1998). On derived equivalences and local structure of blocks of finite groups. Turkish Journal of Mathematics, 22(1), pp. 93–107.
  78. 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.
  79. 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.
  80. Linckelmann, M. (1996). The isomorphism problem for cyclic blocks and their source algebras. Inventiones Mathematicae, 125(2), pp. 265–283. doi:10.1007/s002220050075.
  81. 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.
  82. 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.
  83. Linckelmann, M. (1991). Derived equivalence for cyclic blocks over a P-adic ring. Mathematische Zeitschrift, 207(1), pp. 293–304. doi:10.1007/BF02571389.
  84. 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.
  85. 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.
  86. 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.
  87. 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.
  88. 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.