# 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.

**5**

**0**answers

### Characterizing discrete quantum groups

**3**

**1**answer

### Coinvariants of tensor products of Hopf algebras

**3**

**0**answers

### Hopf algebras structure and quantum affine algebras

**0**

**1**answer

### Showing a product on a character space is continuous

**7**

**1**answer

### What kind of object are the solutions of the Knizhnik-Zamolodchikov Equations

**3**

**0**answers

### Quantum analogue of certain property of compact groups

**8**

**1**answer

### DW, state sum models, and fully extended TQFTs

**4**

**0**answers

### Is there a coproduct on the Weyl algebra which gives the coproduct on $\mathcal{U}_q(\mathfrak{gl}_2)$?

**2**

**0**answers

### Kontsevich integral on tangles and Fubini

**4**

**2**answers

### Abelian category from the category of Hopf algebras

**3**

**1**answer

### Irreducibility of product bicomodules

**2**

**1**answer

### Infinitesimal categories and left duality

**1**

**0**answers

### Proof that for any $u \in L_0$, there exists a $f(q) \in \mathbb{Q}[q]$ for which $f(q)u \in V^{A}$ in global bases theory

**6**

**0**answers

### What is a quantum analogue of the fact that the second fundamental group of every Lie group is trivial?

**3**

**0**answers

### Kashiwara's definition of normal crystal

**3**

**1**answer

### Reduced compact quantum group and left and right multiplication

**7**

**0**answers

### Two algebraic guises of Alternating Sign Matrices: any connection?

**5**

**2**answers

### Characters on Hopf algebras

**7**

**2**answers

### Representations of $D(G)$ as an object in the center of $\operatorname{Rep}(G)$

**8**

**3**answers

### Classification of $\operatorname{Rep} D(G)$

**1**

**0**answers

### Submodules of $V\otimes V^*$

**2**

**0**answers

### Embedding problems on quantum groups？

**2**

**2**answers

### Comultiplication of elements of partition of unity

**3**

**1**answer

### F-symbols for compact Lie groups

**6**

**0**answers

### Example of a commutative, cocommutative, $p$-torsion Hopf algebra which is dualizable but not self-dual?

**8**

**2**answers

### Tannaka-Krein duality in Chari-Pressley's book

**1**

**1**answer

### Some quantities associated to finite dimensional Hopf algebras

**3**

**1**answer

### A submodule of a tensor product of $U_q^{\prime}(\mathfrak{g})$-modules

**0**

**1**answer

### Quantum (group) version of ${\mathbb Z}^n$?

**10**

**3**answers

### Hopf structure on the universal enveloping of a super Lie algebra

**8**

**1**answer

### Image of Comultiplication on Finite Quantum Groups/Hopf Algebras

**4**

**0**answers

### Drinfeld Polynomial for Yangian $Y(\mathfrak{sl}_2)$

**4**

**1**answer

### Invariance of Finite Dimensional Woronowicz $\mathrm{C}^*$-ideals under the Antipode

**3**

**1**answer

### Noncommutative Leray - Hirsch theorem in the context of noncommutative principal bundles

**11**

**0**answers

### Is every finite quantum group a quantum symmetry group?

**8**

**2**answers

### q-difference equations and quantum mechanics

**4**

**1**answer

### A “concrete” example of a one-sided Hopf algebra

**8**

**1**answer

### An inner product approach to Hopf algebras

**5**

**1**answer

### Zero divisors in compact quantum groups

**1**

**0**answers

### almost magic unitary

**2**

**0**answers

### Why are the quantum Fock spaces in FLOTW the same as Uglov's?

**5**

**2**answers

### Indecomposable, non-simple, modules of quantum groups at roots of unity

**5**

**0**answers

### Lusztig's completion for universal enveloping algebra

**25**

**1**answer

### Have the Quantum Group Theorists taught the Group Theorists Anything?

**4**

**0**answers

### Scaling Yetter--Drinfeld Modules

**14**

**1**answer

### P-adic Volume Conjecture

**10**

**1**answer

### Is the quantum $\mathfrak{sl}_3$ invariant stronger than the quantum $\mathfrak{sl}_2$ invariant?

**9**

**0**answers

### Is there a non-Kac complex finite dimensional semisimple Hopf algebra?

**2**

**1**answer

### Coalgebras(or quantum groups) which admit a linear operator satisfying certain functional equation

**4**

**0**answers