Braided quantum groups and their bosonizations in the $C^*$-algebraic framework
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2016
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910497799929856 |
|---|---|
| author | Roy, Sutanu |
| author_facet | Roy, Sutanu |
| contents | We present a general theory of braided quantum groups in the C*-algebraic framework using the language of multiplicative unitaries. Starting with a manageable multiplicative unitary in the representation category of the quantum codouble of a regular quantum group $\mathbb{G}$ we construct a braided C*-quantum group over $\mathbb{G}$ as a C*-bialgebra in the monoidal category of the $\mathbb{G}$-Yetter-Drinfeld C*-algebras. Furthermore, we establish the one to one correspondence between braided C*-quantum groups and C*-quantum groups with projection. Consequently, we generalise the bosonization construction for braided Hopf-algebras of Radford and Majid to braided C*-quantum groups. Several examples are discussed. In particular, we show that the complex quantum plane admits a the braided C*-quantum group structure over the circle group $\mathbb{T}$ and identify its bosonization with the simplified quantum $E(2)$ group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1601_00169 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Braided quantum groups and their bosonizations in the $C^*$-algebraic framework Roy, Sutanu Operator Algebras Quantum Algebra We present a general theory of braided quantum groups in the C*-algebraic framework using the language of multiplicative unitaries. Starting with a manageable multiplicative unitary in the representation category of the quantum codouble of a regular quantum group $\mathbb{G}$ we construct a braided C*-quantum group over $\mathbb{G}$ as a C*-bialgebra in the monoidal category of the $\mathbb{G}$-Yetter-Drinfeld C*-algebras. Furthermore, we establish the one to one correspondence between braided C*-quantum groups and C*-quantum groups with projection. Consequently, we generalise the bosonization construction for braided Hopf-algebras of Radford and Majid to braided C*-quantum groups. Several examples are discussed. In particular, we show that the complex quantum plane admits a the braided C*-quantum group structure over the circle group $\mathbb{T}$ and identify its bosonization with the simplified quantum $E(2)$ group. |
| title | Braided quantum groups and their bosonizations in the $C^*$-algebraic framework |
| topic | Operator Algebras Quantum Algebra |
| url | https://arxiv.org/abs/1601.00169 |