Notes on Yetter-Drinfeld algebras over Hopf algebras
Frank Taipe
TL;DR
This paper introduces a new characterization of Yetter-Drinfeld algebras over finite-dimensional Hopf algebras, establishing its equivalence with the traditional approach and highlighting its role in quantum transformation groupoids.
Contribution
It presents a modern 'only coaction' characterization of Yetter-Drinfeld algebras and proves its equivalence to the standard 'action-coaction' approach.
Findings
Equivalence between 'only coaction' and 'action-coaction' characterizations.
Application of the new characterization in quantum transformation groupoids.
Enhanced understanding of Yetter-Drinfeld algebra structures.
Abstract
In this work, we study another characterization of Yetter-Drinfeld algebras over finite-dimensional Hopf algebras. We show the equivalence between this characterization, called the "only coaction" characterization, and the standard "action-coaction" characterization. This modern approach for Yetter-Drinfeld algebras is one of the key ingredient in a self-dual theory of quantum transformation groupoids arising from actions of quantum groups.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology