# Publishing house / Banach Center Publications / All volumes

## Translations in quantum groups

### Volume 120 / 2020

Banach Center Publications 120 (2020), 151-160 MSC: 20G42, 46L51, 22D25. DOI: 10.4064/bc120-11

#### Abstract

\lt p \gt Let $H$ be the Hopf $C^*$-algebra of continuous functions on a (locally) compact quantum group of either reduced or full type. We show that endomorphisms of $H$ that respect its right regular comodule structure are translations by elements of the largest classical subgroup of $G$. \lt /p \gt \lt p \gt Furthermore, we show that for compact $G$ such an endomorphism is automatically an automorphism regardless of the quantum group norm on the $C^*$-algebra $H$. \lt /p \gt

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