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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 (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
  • 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
  • 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
  • About the site
    ...njecture and to the classification of blocks of finite groups up to Morita equivalence. *record the classification of Morita equivalences as it progresses
    1 KB (207 words) - 13:19, 24 September 2019
  • 5 +^3
    ...group are classified in [[References#A|[AE23]]]. Blocks in the same Morita equivalence class have the same fusion, and so the same inertial quotient, and the same
    9 KB (993 words) - 10:36, 4 October 2023
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