Bulletin of the Belgian Mathematical Society - Simon Stevin

Strictification of weakly equivariant Hopf algebras

Jennifer Maier, Thomas Nikolaus, and Christoph Schweigert

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Abstract

A weakly equivariant Hopf algebra is a Hopf algebra $A$ with an action of a finite group $G$ up to inner automorphisms of $A$. We show that each weakly equivariant Hopf algebra can be replaced by a Morita equivalent algebra $A^{str}$ with a strict action of $G$ and with a coalgebra structure that leads to a tensor equivalent representation category. However, the coproduct of this strictification cannot, in general, be chosen to be unital, so that a strictification of the $G$-action can only be found on a \emph{weak} Hopf algebra $A^{str}$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 2 (2013), 269-285.

Dates
First available in Project Euclid: 23 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1369316544

Digital Object Identifier
doi:10.36045/bbms/1369316544

Mathematical Reviews number (MathSciNet)
MR3082764

Zentralblatt MATH identifier
1291.16024

Subjects
Primary: 16T05: Hopf algebras and their applications [See also 16S40, 57T05] 81R05: Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70]

Keywords
weak Hopf algebra equivariant Hopf algebra strictification

Citation

Maier, Jennifer; Nikolaus, Thomas; Schweigert, Christoph. Strictification of weakly equivariant Hopf algebras. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 2, 269--285. doi:10.36045/bbms/1369316544. https://projecteuclid.org/euclid.bbms/1369316544


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