Hochschild homology and trivial extensions
Petter Andreas Bergh, Dag Oskar Madsen
TL;DR
This paper investigates the Hochschild homology dimension of trivial extensions of algebras, showing it is infinite for certain classes such as selfinjective, local, or graded algebras.
Contribution
It establishes new results linking algebra properties to the Hochschild homology dimension of their trivial extensions.
Findings
Hochschild homology dimension is infinite for selfinjective trivial extensions.
Hochschild homology dimension is infinite for local trivial extensions.
Hochschild homology dimension is infinite for graded trivial extensions.
Abstract
We prove that if an algebra is either selfinjective, local or graded, then the Hochschild homology dimension of its trivial extension is infinite.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology