Duality and products in algebraic (co)homology theories
Niels Kowalzig, Ulrich Kraehmer
TL;DR
This paper explores how a specific algebraic structure called a $ imes_A$-Hopf algebra explains the relationship between products and dualities in algebraic (co)homology theories, unifying various existing results.
Contribution
It introduces a unified framework based on $ imes_A$-Hopf algebras to understand products and dualities across different algebraic (co)homology theories.
Findings
Provides a unified treatment of Hochschild (co)homology results
Connects dualities and products via $ imes_A$-Hopf algebra structure
Generalizes existing theorems in algebraic (co)homology
Abstract
The origin and interplay of products and dualities in algebraic (co)homology theories is ascribed to a -Hopf algebra structure on the relevant universal enveloping algebra. This provides a unified treatment for example of results by Van den Bergh about Hochschild (co)homology and by Huebschmann about Lie-Rinehart (co)homology.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra