Generalized Hopf-Ore extensions
Lan You, Zhen Wang, Huixiang Chen
TL;DR
This paper characterizes when Ore extensions of Hopf algebras can be endowed with a Hopf algebra structure, generalizing Hopf-Ore extensions, and classifies such extensions for enveloping algebras of certain Lie algebras.
Contribution
It introduces generalized Hopf-Ore extensions and provides necessary and sufficient conditions for their existence, extending the theory of Hopf-Ore extensions.
Findings
Derived conditions for Hopf algebra structures on Ore extensions.
Classified generalized Hopf-Ore extensions for specific Lie algebra enveloping algebras.
Extended the framework of Hopf-Ore extensions to a broader class of Hopf algebras.
Abstract
We derive necessary and sufficient conditions for an Ore extension of a Hopf algebra to have a Hopf algebra structure of a certain type. This construction generalizes the notion of Hopf-Ore extension, called a generalized Hopf-Ore extension. We describe the generalized Hopf-Ore extensions of the enveloping algebras of Lie algebras. For some Lie algebras g, the generalized Hopf-Ore extensions of U(g) are classified.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology