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• Category:Morita equivalence classes
  11 members (0 subcategories, 0 files) - 10:24, 31 August 2018
• 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 (502 words) - 13:49, 2 May 2024
• 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 (2,957 words) - 12:29, 2 May 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
• Block library:About
  ...lasses of blocks of finite groups. At its heart will be classifications of classes organised by defect group. The page is held at the University of Manchester
  478 bytes (84 words) - 15:30, 26 August 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
• MediaWiki:Sidebar
  ** Results on classes of groups|Results on classes of groups ** Labelling for Morita equivalence classes|Labelling for classes
  890 bytes (93 words) - 16:32, 26 September 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

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