Difference between revisions of "Morita invariants"
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== Invariants preserved under <math>k</math>-Morita equivalence of blocks of finite groups == | == Invariants preserved under <math>k</math>-Morita equivalence of blocks of finite groups == | ||
| + | |||
| + | * Cartan matrix, up to rearrangement of rows and columns | ||
| + | * Order of defect group | ||
| + | * Exponent of defect group<ref>See (78) of [[References#K|[Ku91]]]</ref> | ||
| + | * <math>p</math>-rank of defect group<ref>See Corollary 4 of [[References#A|[AE81]]], attributed to Donovan</ref> | ||
== Invariants preserved under <math>\mathcal{O}</math>-Morita equivalence of blocks of finite groups == | == Invariants preserved under <math>\mathcal{O}</math>-Morita equivalence of blocks of finite groups == | ||
Revision as of 09:13, 4 January 2019
Contents
- 1 Invariants preserved under Morita equivalence of blocks of f.d. [math]k[/math]-algebras
- 2 Invariants preserved under [math]k[/math]-Morita equivalence of blocks of finite groups
- 3 Invariants preserved under [math]\mathcal{O}[/math]-Morita equivalence of blocks of finite groups
- 4 Invariants preserved under basic Morita equivalence of blocks of finite groups[3]
- 5 Invariants preserved under splendid Morita equivalence of blocks of finite groups
- 6 Notes
Invariants preserved under Morita equivalence of blocks of f.d. [math]k[/math]-algebras
- Number of isomorphism classes of simple modules
- Isomorphism type of centre of algebra, and so dimension of centre
- Loewy structure and socle structure
Invariants preserved under [math]k[/math]-Morita equivalence of blocks of finite groups
- Cartan matrix, up to rearrangement of rows and columns
- Order of defect group
- Exponent of defect group[1]
- [math]p[/math]-rank of defect group[2]
