Basic Morita equivalences and a conjecture of Sasaki for cohomology of block algebras of finite groups

2015/06/14 by Constantin-Cosmin Todea, C. C. Todea, Todea, C. C.
Mathematics · #16EXX #20C20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #math.KT #math.RT #msc:16EXX #msc:20C20

paper · pdf · doi:10.48550/arxiv.1506.04387

arxiv created 2015/06/14 · openalex publication_date 2015/06/14 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show, using basic Morita equivalences between block algebras of finite groups, that the Conjecture of H. Sasaki from [9] is true for a new class of blocks called nilpotent covered blocks. When this Conjecture is true we define some transfer maps between cohomology of block algebras and we analyze them through transfer maps between Hochschild cohomol- ogy algebras.

Related

• Morita Contexts, Idempotents, and Hochschild Cohomology - with Applications to Invariant Rings -
• A reduction theorem for non-vanishing of Hochschild cohomology of block algebras and Happel's property
• Infinitely many algebras derived equivalent to a block
• Morita Equivalence Classes of Tame Blocks of Finite Groups
• Morita Equivalence of Brandt Semigroup Algebras