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• Glossary
  === Basic Morita/stable equivalence === Morita/stable equivalence of blocks induced by a bimodule which has endopermutation source.
  5 KB (841 words) - 23:02, 18 November 2020
• C(3^n)
  ...Brauer trees]]. For <math>n=1</math> there are just two Morita equivalence classes (see [[C3|<math>C_3</math>]]).
  2 KB (257 words) - 23:34, 2 January 2019
• 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
• C7
  ...<math>k</math>-Morita equivalence classes lift to <math>\mathcal{O}</math>-classes.
  4 KB (465 words) - 12:58, 22 November 2018
• M(8,4,3)
  |k-morita-frob = 1 |defect-morita-inv? = Yes
  2 KB (290 words) - 15:51, 3 June 2021
• M(8,3,4)
  |k-morita-frob = 1 |defect-morita-inv? = Yes
  2 KB (218 words) - 17:51, 4 October 2018
• (C2)^4
  ...lossary#CFSG|CFSG]]. Each of the sixteen <math>k</math>-Morita equivalence classes lifts to an unique class over <math>\mathcal{O}</math>. The possibilities f ...\times C_3</math> || || ||1 ||1 ||Non-principal faithful block. Cannot be Morita equivalent to a principal block of any finite group.
  4 KB (524 words) - 18:39, 9 December 2019
• M(16,2,2)
  |k-morita-frob = 1 |defect-morita-inv? = Yes
  2 KB (237 words) - 10:57, 28 July 2019
• M(8,3,6)
  |k-morita-frob = 1 |defect-morita-inv? = Yes
  2 KB (232 words) - 21:48, 4 October 2018
• M(8,3,5)
  |k-morita-frob = 1 |defect-morita-inv? = Yes
  2 KB (228 words) - 22:11, 4 October 2018
• M(8,4,2)
  |k-morita-frob = 1 |defect-morita-inv? = Yes
  2 KB (265 words) - 09:40, 24 May 2022
• C3xC3
  ...rita equivalence class for each of these <math>k</math>-Morita equivalence classes as they may also contain non-principal blocks. Some Picard groups calculate *Determine whether <math>B_6(k(2.M_{22}))</math> is Morita equivalent to <math>(C_3 \times C_3):Q_8</math>.
  6 KB (781 words) - 10:45, 24 May 2022
• SD16
  ...#M|[Mac]]]: A block of the Monster group could be in one or other of these classes.</ref> All Morita equivalence classes with three simple modules are derived equivalent over <math>k</math> by [[R
  3 KB (385 words) - 14:34, 4 August 2022
• Q16
  ...</math>-Morita equivalence classes lift to unique <math>\mathcal{O}</math>-classes by [[References|[Ei16]]], but otherwise the classification with respect to
  3 KB (368 words) - 12:43, 26 November 2018
• M(16,10,2)
  |k-morita-frob = 1 |defect-morita-inv? = Yes
  2 KB (254 words) - 09:31, 5 December 2018
• Groups of perfect self-isometries
  ...nces|[EL18c]]]) and in the calculation of extensions of Morita equivalence classes from normal subgroups of index <math>p</math> (see for example [[References
  905 bytes (153 words) - 10:40, 6 December 2018
• Tame blocks
  ...g finite or infinite representation type and of being tame or wild are all Morita invariants. ...classification of finite simple groups to classify such blocks up to Puig equivalence in [[References#C|[CEKL11]]].
  3 KB (427 words) - 19:28, 9 November 2022
• Morita invariants
  == Invariants preserved under Morita equivalence of blocks of f.d. <math>k</math>-algebras == * Number of isomorphism classes of simple modules
  2 KB (267 words) - 12:40, 2 May 2024
• MNA(2,2)
  ...ian <math>2</math>-groups. The <math>\mathcal{O}</math>-Morita equivalence classes are classified in [[References#E|[EKS12]]].
  938 bytes (132 words) - 16:46, 28 January 2019
• (C2)^5
  ...e [[Glossary#CFSG|CFSG]]. Each of the 34 <math>k</math>-Morita equivalence classes lifts to an unique class over <math>\mathcal{O}</math>. The known Picard gr ...<math>C_3 \times C_3</math> || || ||1 ||1 ||Non-principal block. Cannot be Morita equivalent to a principal block of any finite group.
  6 KB (825 words) - 10:18, 17 May 2022

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