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Results tagged with quantum-groups
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user 124549
Questions about algebraic structures known as quantum groups, and their categories of representations. Quasitriangular Hopf algebras and their Drinfel'd twists, triangular Hopf algebras, $C^\star$ quantum groups, h-adic quantum groups, various semisimplified categories at roots of unity which are called "quantum groups", bicrossproduct quantum groups, and quantum groups coming from braided tensor categories.
10
votes
1
answer
778
views
DW, state sum models, and fully extended TQFTs
I am interested in state sum models and their relations with some other of TQFTs, especially the fully extended TQFTs and the Dijkgraaf-Witten TQFTs (generalized, in the sense that finite-group-bundle …
- 5,230
8
votes
3
answers
516
views
Classification of $\operatorname{Rep} D(G)$
Let $G$ be a finite group and $D(G)$ its quantum double. Its finite dimensional complex representations are classified in this Dijkgraaf et al. Quasi-Quantum Groups Related To Orbifold Models. However …
- 5,230
7
votes
3
answers
636
views
Representations of $D(G)$ as an object in the center of $\operatorname{Rep}(G)$
Let $G$ be a finite group and $D(G)$ its quantum double. As in my previous question, a typical irreducible representation (finite dimensional over $\mathbb{C}$) is labeled by $(\theta,\pi)$, where $\t …
- 5,230
3
votes
Classification of $\operatorname{Rep} D(G)$
This is a study note that spells out @Konstantinos's answer
explicitly.
Preface
Our goal is to classify all finite dimensional representations over
the complex number field for the quantum double …
- 5,230
2
votes
Representations of $D(G)$ as an object in the center of $\operatorname{Rep}(G)$
This is my study note that spells out @Adrien 's answer to 1) and 2). As suggested by @Adrien, we will follow Kassel's Quantum Groups, mainly chapter XIII.5. It is a very detailed account.
Explicit e …
- 5,230