# Questions tagged [quantum-groups]

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.

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### Anticommutation of convolution products on trace class operators of quantum groups

This question was originally posted to MathStackExchange. Let $\mathbb{G}$ be a locally compact quantum group and let $W$ and $V$ be the left and right fundamental unitaries, i.e., they implement the ...
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Before asking my question, let me introduce the relevant terminology. Throughout, let $(A, \Delta)$ be a compact quantum group. Definition: A representation $v$ on the Hilbert space $H$ is an element $... 1answer 149 views ### Constructing intertwiners between representations of compact quantum groups Consider the following paper by Van Daele en Maes Notes on compact quantum groups. For convenience of the reader, here is a picture of the relevant section: (1) How is compact operator defined in ... 1answer 80 views ### Extending$*$-morphisms to the multiplier algebras I'm reading the following fragment in the paper "Notes on compact quantum groups": While I'm familiar with the multiplier algebra (constructed via double centralizers) and its universal ... 2answers 211 views ### Convolution of functionals on compact quantum group Let$\mathbb{G}= (A, \Delta)$be a ($C^*$-algebraic) compact quantum group. In a paper I'm reading, the space$A^*= B(A, \mathbb{C})$obtains a product$$\omega_1*\omega_2:= (\omega_1\otimes \omega_2) ... 0answers 164 views ### Are the finite quantum permutation groups, weakly group-theoretical? Wang defined in Quantum symmetry groups of finite spaces a notion of quantum automorphism group. The application to a finite space of$n$elements is called the quantum permutation group of$n$... 0answers 168 views ### Where can I find Drinfeld's original papers on quantum groups? Let$\mathfrak{g}$be a semisimple Lie algebra. Let$U_h(\mathfrak{g})$be the Drinfeld-Jimbo quantum group, i.e. the$\mathbb{C}[[h]]$-algebra topologically generated by$X_i,Y_i,H_i$where$1\leq i\...
An adjunction of the form $\mathrm{Hom}(A \otimes X, Y) \cong \mathrm{Hom}(X, A^* \otimes Y)$ in a rigid monoidal category is sometimes called Frobenius reciprocity. Is there a result that unifies ...