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  • We use two compatible systems for labelling Morita equivalence classes of blocks of finite groups with respect to an algebraically closed field <m Note that it is not known that the isomorphism class of a defect group is a Morita invariant, so it could be that M(x,y1,z1)=M(x,y2,z2) for some <math>(y1,z1)
    3 KB (477 words) - 10:08, 3 October 2023

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  • <div style="font-size:95%;">of Morita equivalence classes</div> ...re|Donovan's conjecture]] and for the classification of Morita equivalence classes of blocks with a given defect group. The intention is to eventually make th
    4 KB (502 words) - 12:49, 2 May 2024
  • ...math>-group. Then there are only finitely many possible Morita equivalence classes for blocks of <math>kG</math> for finite groups G with defect group isomorp ...math>-group. Then there are only finitely many possible Morita equivalence classes for blocks of <math>\mathcal{O} G</math> for finite groups G with defect gr
    6 KB (970 words) - 15:15, 21 August 2020
  • '''Classification of Morita equivalences for blocks with a given defect group''' ...rn. [[Generic classifications by p-group class|Generic classifications for classes of p-groups can be found here]].
    33 KB (3,797 words) - 18:59, 10 January 2024
  • ...alence classes|this page]] for the labelling system for Morita equivalence classes. Please try to follow existing classifications for labelling where possible |k-morita-frob =
    3 KB (364 words) - 16:32, 9 December 2019
  • There are two <math>\mathcal{O}</math>-Morita equivalence classes, accounting for all the possible Brauer trees.
    1 KB (154 words) - 10:20, 22 November 2018
  • There are three <math>\mathcal{O}</math>-Morita equivalence classes, accounting for all the possible Brauer trees.
    1 KB (168 words) - 10:27, 22 November 2018
  • ...and C. W. Eaton''', [https://arxiv.org/abs/2310.02150 ''Morita equivalence classes of blocks with extraspecial defect groups <math>p_+^{1+2}</math>''], [https ...'''C. G. Ardito''', [https://arxiv.org/abs/1908.02652 ''Morita equivalence classes of blocks with elementary abelian defect groups of order 32''], J. Algebra
    21 KB (2,957 words) - 11:29, 2 May 2024
  • |<math>l(B)</math> || Number of isomorphism classes of simple <math>B</math>-modules || | <math>{\rm mf_k(B)}</math> || The Morita-Frobenius number of <math>kB</math> || [[References|[Ke04] ]]
    3 KB (444 words) - 17:45, 9 December 2019
  • ...neq 2</math><ref>When <math>l(B) \neq 2</math>, each <math>k</math>-Morita equivalence class lifts uniquely to <math>\mathcal{O}</math> by [[References|[Ei16]]].< ...classes involved are known. This is only known for elements of the Morita equivalence class which occur as blocks of groups in that class.
    5 KB (727 words) - 09:06, 24 October 2023
  • There are six <math>\mathcal{O}</math>-Morita equivalence classes, accounting for all the possible Brauer trees.
    1 KB (205 words) - 10:28, 22 November 2018
  • ...phism type of a defect group|Is the isomorphism type of the defect group a Morita invariant?]] - no (see [[References#G|[GMdelR21]]]) * Is every Morita equivalence between <math>\mathcal{O}</math>-blocks endopermutation source?
    1 KB (178 words) - 11:30, 21 June 2021
  • ...t Morita equivalence classes amongst blocks of groups belonging to certain classes or families, for example groups of Lie type or <math>p</math>-solvable grou
    196 bytes (31 words) - 15:35, 5 September 2018
  • ...s not known which give rise to <math>\mathcal{O}</math>-Morita equivalence classes.
    2 KB (229 words) - 10:31, 22 November 2018
  • ...r87] ]]). The Morita equivalence classes lift to unique Morita equivalence classes over <math>\mathcal{O}</math> by [[References#H|[HKL07]]], [[References#E|[
    1 KB (184 words) - 08:35, 24 May 2022
  • |k-morita-frob = 1 |O-morita-frob = 1
    2 KB (225 words) - 14:59, 7 October 2018
  • |k-morita-frob = 1 |defect-morita-inv? = Yes
    2 KB (230 words) - 12:18, 9 September 2018
  • |k-morita-frob = 1 |defect-morita-inv? = Yes
    2 KB (309 words) - 14:47, 4 January 2019
  • |k-morita-frob = 1 |defect-morita-inv? = Yes
    3 KB (348 words) - 15:29, 22 November 2018
  • ...have classifications or have general results concerning Morita equivalence classes. Blocks with fusion trivial defect groups must be nilpotent and so Morita equivalent to the group algebra of a defect group by [[References#P|[Pu88]]
    11 KB (1,772 words) - 11:15, 9 January 2024
  • There are three <math>\mathcal{O}</math>-Morita equivalence classes, accounting for all the possible Brauer trees.
    1 KB (148 words) - 10:26, 22 November 2018

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