On the cohomology of a smash product of Hopf algebras
Mitja Mastnak
TL;DR
This paper develops a five-term sequence for computing the low-degree cohomology of smash products of cocommutative Hopf algebras, extending Tahara's results for group semi-direct products.
Contribution
It generalizes Tahara's cohomology sequence from group semi-direct products to smash products of cocommutative Hopf algebras.
Findings
Established a five-term cohomology sequence for cocommutative Hopf algebra smash products.
Extended classical group cohomology results to Hopf algebra context.
Provided tools for analyzing the cohomology of complex algebraic structures.
Abstract
A five term sequence for the low degree cohomology of a smash product of (cocommutative) Hopf algebras is obtained, generalizing that of Tahara for a semi-direct product of groups.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology