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5 votes
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606 views

Weak Hopf algebra structure on twisted group algebra

A (normalized) $2$-cocycle on a finite group $G$ with values in $S^1$ is a map $\sigma:G\times G\rightarrow S^1$ such that $$\sigma(g,h)\sigma(gh,k)=\sigma(h,k)\sigma(g,hk)$$ and $$\sigma(g,e)=\sigma(...
Keshab Bakshi's user avatar
6 votes
2 answers
256 views

Are there examples of finite-dimensional weak Hopf C*-algebras with non-involutive antipode?

For finite-dimensional (non-weak) Hopf C*-algebras it is known that the antipode is always involutive, as claimed e.g. in https://arxiv.org/pdf/1007.5283.pdf. I couldn't find the same statement for ...
Andi Bauer's user avatar
  • 3,001
7 votes
0 answers
331 views

An alternative Cauchy theorem on Hopf algebras

Let $\mathbb{A}$ be a finite dimensional Hopf ${\rm C}^{\star}$-algebra. There already exists a generalization of Cauchy theorem using exponent, see [KSZ06]. We are interesting in an alternative ...
Sebastien Palcoux's user avatar