Hopf automorphisms and twisted extensions
Susan Montgomery, Maria D. Vega, and Sarah Witherspoon
TL;DR
This paper explores the structure and properties of a Hopf algebra formed via a group action on another Hopf algebra, revealing connections between various algebraic invariants and studying its module category.
Contribution
It introduces applications of Molnar's smash coproduct Hopf algebra, linking its invariants to those of the original algebra and analyzing its module category.
Findings
Connections between exponent and Frobenius-Schur indicators of the smash coproduct and the original algebra
Relationships between twisted exponents and twisted Frobenius-Schur indicators
Analysis of the module category of the smash coproduct
Abstract
We give some applications of a Hopf algebra constructed from a group acting on another Hopf algebra A as Hopf automorphisms, namely Molnar's smash coproduct Hopf algebra. We find connections between the exponent and Frobenius-Schur indicators of a smash coproduct and the twisted exponents and twisted Frobenius-Schur indicators of the original Hopf algebra A. We study the category of modules of the smash coproduct.
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