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• Labelling for Morita equivalence classes
  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) - 11:08, 3 October 2023

Page text matches

• Main Page
  <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 (500 words) - 22:10, 18 November 2020
• Statements of conjectures
  ...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) - 16:15, 21 August 2020
• Classification by p-group
  '''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) - 19:59, 10 January 2024
• Guide to contributing
  ...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) - 17:32, 9 December 2019
• C3
  There are two <math>\mathcal{O}</math>-Morita equivalence classes, accounting for all the possible Brauer trees.
  1 KB (154 words) - 11:20, 22 November 2018
• C9
  There are three <math>\mathcal{O}</math>-Morita equivalence classes, accounting for all the possible Brauer trees.
  1 KB (168 words) - 11:27, 22 November 2018
• References
  ...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 (2,953 words) - 12:20, 9 January 2024
• Notation
  |<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) - 18:45, 9 December 2019
• Status of Donovan's conjecture
  ...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) - 10:06, 24 October 2023
• C5
  There are six <math>\mathcal{O}</math>-Morita equivalence classes, accounting for all the possible Brauer trees.
  1 KB (205 words) - 11:28, 22 November 2018
• Open problems
  ...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) - 12:30, 21 June 2021
• Results on classes of groups
  ...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) - 16:35, 5 September 2018
• C25
  ...s not known which give rise to <math>\mathcal{O}</math>-Morita equivalence classes.
  2 KB (229 words) - 11:31, 22 November 2018
• Q8
  ...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) - 09:35, 24 May 2022
• M(3,1,1)
  |k-morita-frob = 1 |O-morita-frob = 1
  2 KB (225 words) - 15:59, 7 October 2018
• M(2,1,1)
  |k-morita-frob = 1 |defect-morita-inv? = Yes
  2 KB (230 words) - 13:18, 9 September 2018
• M(4,2,2)
  |k-morita-frob = 1 |defect-morita-inv? = Yes
  2 KB (309 words) - 15:47, 4 January 2019
• M(4,2,3)
  |k-morita-frob = 1 |defect-morita-inv? = Yes
  3 KB (348 words) - 16:29, 22 November 2018
• Generic classifications by p-group class
  ...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) - 12:15, 9 January 2024
• C27
  There are three <math>\mathcal{O}</math>-Morita equivalence classes, accounting for all the possible Brauer trees.
  1 KB (148 words) - 11:26, 22 November 2018

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