Translations in quantum groups
| Autor: | Alexandru Chirvasitu |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Endomorphism Quantum group Mathematics::Rings and Algebras 010102 general mathematics Mathematics - Operator Algebras Structure (category theory) Type (model theory) Automorphism 01 natural sciences Comodule Norm (mathematics) Mathematics - Quantum Algebra 0103 physical sciences FOS: Mathematics Quantum Algebra (math.QA) General Earth and Planetary Sciences 010307 mathematical physics Compact quantum group 20G42 46L51 22D25 0101 mathematics Operator Algebras (math.OA) General Environmental Science Mathematics |
| Zdroj: | Banach Center Publications. 120:151-160 |
| ISSN: | 1730-6299 0137-6934 |
| Popis: | 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 largest classical subgroup of $G$. Furthermore, we show that for compact $G$ such an endomorphism is automatically an automorphism regardless of the quantum group norm on the $C^*$-algebra $H$; this answers a question of Piotr M. Hajac. Comment: 8 pages + references; changes reflecting referee suggestions: proof of Theorem 2.13 changed so as to appeal to reference [6] |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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