Difference between revisions of "Morita invariants"

From Block library
Jump to: navigation, search
(Created page with "== Invariants preserved under Morita equivalence of blocks of <math>k</math>-algebras == == Invariants preserved under <math>k</math>-Morita equivalence of blocks of finite g...")
 
Line 1: Line 1:
== Invariants preserved under Morita equivalence of blocks of <math>k</math>-algebras ==
+
[[Image:under-construction.png|50px|left]]
 +
 
 +
== 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 ==
 
== Invariants preserved under <math>k</math>-Morita equivalence of blocks of finite groups ==

Revision as of 17:57, 3 January 2019

Under-construction.png

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

Invariants preserved under [math]\mathcal{O}[/math]-Morita equivalence of blocks of finite groups

Invariants preserved under basic Morita equivalence of blocks of finite groups[1]

Invariants preserved under splendid Morita equivalence of blocks of finite groups

Notes

  1. Note that by [KL18], if [math]k[/math]-blocks are basic Morita equivalent, then the corresponding [math]\mathcal{O}[/math]-blocks are Morita equivalent