(Co)homology of crossed products in weak contexts

2018/11/07 by Jorge A. Guccione, Guccione, Jorge A., Juan J. Guccione +3
Mathematics · #16E40 #16T05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1811.02927

openalex publication_date 2018/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain a mixed complex simpler than the canonical one the computes the type cyclic homologies of a crossed product with invertible cocycle A×_ρ^f H, of a weak module algebra A by a weak Hopf algebra H whose unit cocommutes. This complex is provided with a filtration. The spectral sequence of this filtration generalizes the spectral sequence obtained in \citeCGG. When f takes its values in a separable subalgebra of A that satisfies suitable conditions, the above mentioned mixed complex is provided with another filtration, whose spectral sequence generalize the Feigin-Tsygan spectral sequence.

Related

• (Co)homology of Crossed Products by Weak Hopf Algebras
• Cyclic homology of crossed products
• On the Cyclic Homology of Hopf Crossed Products
• Hopf Algebra Equivariant Cyclic Homology and Cyclic Homology of Crossed Product Algebras
• Hochschild (co)homology of Hopf crossed products