Homology of Epsilon-Strongly Graded Algebras

2025/07/22 by Emmanuel Jerez, Jerez, Emmanuel
Mathematics · #16W50 #18G40 #18G60 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Primary 16E40 #Rings and Algebras (math.RA) #Secondary 16W22

paper · pdf · doi:10.48550/arxiv.2507.16778

openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a group and S a unital epsilon-strongly G-graded algebra. We construct spectral sequences converging to the Hochschild (co)homology of S. Each spectral sequence is expressed in terms of the partial group (co)homology of G with coefficients in the Hochschild (co)homology of the degree-one component of S. Moreover, we show that the homology spectral sequence decomposes according to the conjugacy classes of G, and, by means of the globalization functor, its E²-page can be identified with the ordinary group homology of suitable centralizers.

Citations

• The twisted partial group algebra and (co)homology of partial crossed products
• (Co)Homology of Partial Smash Products
• Very good gradings on matrix rings are epsilon-strong
• Homology and cohomology via the partial group algebra
• The graded structure of algebraic Cuntz-Pimsner rings
• Epsilon-strongly graded rings, separability and semisimplicity

Related

• A spectral sequence for the homology of a finite algebraic delooping
• Global Hochschild (co-)homology of singular spaces
• On the homology of partial group representations
• Spaces of homomorphisms, formality and Hochschild homology
• Spectral sequences for the cyclic cohomology of differential graded algebras