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arXiv · 1811.02927

(Co)homology of crossed products in weak contexts

Jorge A. Guccione·Juan J. Guccione·Christian Valqui
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Abstract

We obtain a mixed complex simpler than the canonical one the computes the type cyclic homologies of a crossed product with invertible cocycle $A\times_ρ^f H$, 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 \cite{CGG}. 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.

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Jorge A. Guccione, Juan J. Guccione, Christian Valqui. 2021-03-01. (Co)homology of crossed products in weak contexts. https://arxiv.org/abs/1811.02927

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