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arXiv · 1511.08783

Inner Actions of Weak Hopf Algebras

Dirceu Bagio·Daiana Flôres·Alveri Sant'Ana
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Abstract

Let $R$ be an associative ring and $e,f$ idempotent elements of $R$. In this paper we introduce the notion of $(e,f)$-invertibility for an element of $R$ and use it to define inner actions of weak Hopf algebras. Given a weak Hopf algebra $H$ and an algebra $A$, we present sufficient conditions for $A$ to admit an inner action of $H$. We also prove that if $A$ is a left $H$-module algebra then $H$ acts innerly on the smash product $A\#H$ if and only if $H$ is a quantum commutative weak Hopf algebra.

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Dirceu Bagio, Daiana Flôres, Alveri Sant'Ana. 2015-11-27. Inner Actions of Weak Hopf Algebras. https://doi.org/10.1142/s0219498817501183

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