Ambiskew Hopf Algebras
Kenneth A. Brown, Monica Macauley
TL;DR
This paper establishes conditions under which ambiskew polynomial algebras over Hopf algebras can be endowed with a compatible Hopf algebra structure, including calculations of their coradical filtration and numerous examples.
Contribution
It provides necessary and sufficient conditions for ambiskew polynomial algebras over Hopf algebras to be Hopf algebras with skew primitive variables, expanding understanding of their structure.
Findings
Conditions for Hopf algebra extension are characterized.
Coradical filtration of these algebras is computed.
Multiple examples illustrating the theory are provided.
Abstract
Necessary and sufficient conditions are obtained for an ambiskew polynomial algebra A over a Hopf k-algebra R to possess the structure of a Hopf algebra extending that of R, in which the added variables X+ and X- are skew primitive. The coradical filtration is calculated, many examples are described, and properties determined.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Operator Algebra Research