The standard construction for cocycle twisted and braided tensor product W$^*$-algebras
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| Format: | Preprint |
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2025
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| author | De Commer, K. Krajczok, J. |
| author_facet | De Commer, K. Krajczok, J. |
| contents | Given a locally compact quantum group $\mathbb{G}$ and a (generalized) dual unitary $2$-cocycle $\hatΩ$, any W$^*$-algebra $A$ with a $\mathbb{G}$-action can be twisted into a new W$^*$-algebra $A_{\hatΩ}$ with an action by the cocycle twist $\mathbb{G}_{\hatΩ}$ of $\mathbb{G}$. We show how, in general, the standard space $L^2(A_{\hatΩ})$, with its standard $\mathbb{G}_{\hatΩ}$-representation, can be seen as a twist of $L^2(A)$ with its standard $\mathbb{G}$-representation. We then apply this general result in the special case of (generalized) Drinfeld doubles. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_00595 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The standard construction for cocycle twisted and braided tensor product W$^*$-algebras De Commer, K. Krajczok, J. Operator Algebras Primary 46L67, Secondary 46L55, 46L06 Given a locally compact quantum group $\mathbb{G}$ and a (generalized) dual unitary $2$-cocycle $\hatΩ$, any W$^*$-algebra $A$ with a $\mathbb{G}$-action can be twisted into a new W$^*$-algebra $A_{\hatΩ}$ with an action by the cocycle twist $\mathbb{G}_{\hatΩ}$ of $\mathbb{G}$. We show how, in general, the standard space $L^2(A_{\hatΩ})$, with its standard $\mathbb{G}_{\hatΩ}$-representation, can be seen as a twist of $L^2(A)$ with its standard $\mathbb{G}$-representation. We then apply this general result in the special case of (generalized) Drinfeld doubles. |
| title | The standard construction for cocycle twisted and braided tensor product W$^*$-algebras |
| topic | Operator Algebras Primary 46L67, Secondary 46L55, 46L06 |
| url | https://arxiv.org/abs/2508.00595 |