Morita invariants
Revision as of 11:40, 2 May 2024 by Charles Eaton (talk | contribs)
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 (hence, in the case of [math]k[/math]-blocks of finite groups, the number of irreducible characters associated to the corresponding [math]\mathcal{O}[/math]-block)
- Loewy structure and socle structure
Invariants preserved under [math]k[/math]-Morita equivalence of blocks of finite groups
- Invariants listed above
- 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]
Invariants preserved under [math]\mathcal{O}[/math]-Morita equivalence of blocks of finite groups
- Invariants listed above
- Number [math]k_h(B)[/math] of irreducible characters of a given height [math]h[/math]
- Decomposition matrix, up to rearrangement of rows and columns
Invariants preserved under basic Morita equivalence of blocks of finite groups[3]
- Invariants listed above
- Isomorphism type of a defect group[4]
- Fusion system of the block[5]
Invariants preserved under splendid Morita equivalence of blocks of finite groups
- Invariants listed above
- Source algebra
