The action of the Nakayama automorphism of a Frobenius algebra on Hochschild cohomology
Mariano Su\'arez-\'Alvarez
TL;DR
This paper proves that the Nakayama automorphism acts trivially on Hochschild cohomology in Frobenius algebras, enabling the construction of algebraic invariants related to automorphisms and derivations.
Contribution
It establishes the trivial action of the Nakayama automorphism on Hochschild cohomology and introduces methods to construct related invariants.
Findings
Nakayama automorphism acts trivially on Hochschild cohomology
Construction of invariants associated with automorphisms and derivations
Application to Frobenius algebra classification
Abstract
We prove that the Nakayama automorphism of a Frobenius algebra acts trivially on the Hochschild cohomology of the algebra. As an application of this fact, we show how to construct certain invariants attached to such algebras, and to their automorphisms and derivations.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Finite Group Theory Research · Algebraic structures and combinatorial models