Generalized Yetter-Drinfel'd module categories for regular multiplier Hopf algebras

Abstract

For a regular multiplier Hopf algebra $A$, the Yetter-Drinfel'd module category ${}_A{\mathcal{YD}}^A$ is equivalent to the centre $Z({}_A\mathcal{M})$ of the unital left $A$-module category ${}_A\mathcal{M}$. Then we introduce the generalized $(\alpha ,\beta )$-Yetter-Drinfel'd module categories ${}_A{\mathcal{G}\mathcal{YD}}^A(\alpha ,\beta )$, which are treated as components of a braided $T$-category. Especially when $A$ is a coFrobenius Hopf algebra, ${}_A{\mathcal{YD}}^A(\alpha ,\beta )$ is isomorphic to the unital $\hat{A}\bowtie A(\alpha ,\beta )$-module category ${}_{\hat{A}\bowtie A(\alpha ,\beta )}\mathcal{M}$. Finally for a Yetter-Drinfel'd $A$-module algebra $H$, we introduce Yetter-Drinfel'd $(H,A)$-module category, which is a monoidal.

15 pages

References in corpus (1)

• Tools for working with multiplier Hopf algebras