Quantum $SL(2,\mathbb{R})$ and its irreducible representations
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2021
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911913748725760 |
|---|---|
| author | De Commer, Kenny Talla, Joel Right Dzokou |
| author_facet | De Commer, Kenny Talla, Joel Right Dzokou |
| contents | We define for real $q$ a unital $*$-algebra $U_q(\mathfrak{sl}(2,\mathbb{R}))$ quantizing the universal enveloping $*$-algebra of $\mathfrak{sl}(2,\mathbb{R})$. The $*$-algebra $U_q(\mathfrak{sl}(2,\mathbb{R}))$ is realized as a $*$-subalgebra of the Drinfeld double of $U_q(\mathfrak{su}(2))$ and its dual Hopf $*$-algebra $\mathcal{O}_q(SU(2))$, generated by the equatorial Podleś sphere coideal $*$-subalgebra $\mathcal{O}_q(K\backslash SU(2))$ of $\mathcal{O}_q(SU(2))$ and its associated orthogonal coideal $*$-subalgebra $U_q(\mathfrak{k}) \subseteq U_q(\mathfrak{su}(2))$. We then classify all the irreducible $*$-representations of $U_q(\mathfrak{sl}(2,\mathbb{R}))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_04258 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Quantum $SL(2,\mathbb{R})$ and its irreducible representations De Commer, Kenny Talla, Joel Right Dzokou Quantum Algebra Representation Theory 17B37, 46L67, 20G42 We define for real $q$ a unital $*$-algebra $U_q(\mathfrak{sl}(2,\mathbb{R}))$ quantizing the universal enveloping $*$-algebra of $\mathfrak{sl}(2,\mathbb{R})$. The $*$-algebra $U_q(\mathfrak{sl}(2,\mathbb{R}))$ is realized as a $*$-subalgebra of the Drinfeld double of $U_q(\mathfrak{su}(2))$ and its dual Hopf $*$-algebra $\mathcal{O}_q(SU(2))$, generated by the equatorial Podleś sphere coideal $*$-subalgebra $\mathcal{O}_q(K\backslash SU(2))$ of $\mathcal{O}_q(SU(2))$ and its associated orthogonal coideal $*$-subalgebra $U_q(\mathfrak{k}) \subseteq U_q(\mathfrak{su}(2))$. We then classify all the irreducible $*$-representations of $U_q(\mathfrak{sl}(2,\mathbb{R}))$. |
| title | Quantum $SL(2,\mathbb{R})$ and its irreducible representations |
| topic | Quantum Algebra Representation Theory 17B37, 46L67, 20G42 |
| url | https://arxiv.org/abs/2107.04258 |