(Co)homology of Crossed Products by Weak Hopf Algebras

2019/07/09 by Guccione, Jorge A., Guccione, Juan J., Valqui, Christian
#16E40 #16T05 #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1907.05229

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. 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 in weak contexts
• 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