# 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.

**2**

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

**5**

**2**answers

### Classifying Hopf algebras that admit a single irreducible comodule

**4**

**1**answer

### Name for a Hopf algebra whose only grouplike element is the identity?

**4**

**1**answer

### Hopf algebra that is unimodular and counimodular but not involutory

**5**

**0**answers

### Classification of connected finite affine type A crystals

**3**

**1**answer

### Nonstandard Podles spheres as $U_c(\frak{h})$ invariants

**3**

**1**answer

### The adjoint representation of $U_q({\frak sl}_2)$ on itself

**10**

**2**answers

### What is the discrete quantum group associated to a compact group?

**12**

**1**answer

### Representations of $U_q(\mathfrak{sl}(2))$ as differential / difference operators

**5**

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### Induction for quantum group

**9**

**2**answers

### Is there a nice q-analogue of the Jacobi identity in a quantized enveloping algebra?

**6**

**1**answer

### Tensor representations of the quantum algebra $U_q(\mathfrak{sl}(2))$ at the roots of unity

**3**

**0**answers

### Fiber product of group rings

**3**

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### Quantum orbit method at roots of unity

**4**

**3**answers

### Name for a Hopf algebra admitting no non-trivial 1-dimensional comodule

**0**

**1**answer

### Quantum double vs Quantum group

**3**

**1**answer

### quantum affine $gl_2$

**5**

**2**answers

### Low dimensional noncommutative non-cocommutative Hopf algebras

**9**

**1**answer

### The double cover in the classical limit of $U_q(\mathfrak{sl}_2)$

**4**

**0**answers

### Why does Kashiwara define $U_q(\mathfrak{g})$ over $\mathbb{Q}(q)$ rather than $\mathbb{C}(q)$?

**2**

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### Involutive solutions to the Yang-Baxter equation (and triangular Hopf algebras)

**1**

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### Superfluous axioms for ribbon Hopf algebra

**8**

**1**answer

### Trying to understand "a refinement of the Peter–Weyl theorem" by Lusztig

**18**

**2**answers

### Why does Drinfeld Unitarization work?

**3**

**1**answer

### What is the determinant of the R-matrix defining the colored Jones polynomial?

**1**

**1**answer

### A comodule algebra map from a Hopf algebra to itself

**2**

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### Relation Hopf categories and categorified quantum groups

**6**

**1**answer

### Morphisms between compact quantum groups

**5**

**1**answer

### Matrix coefficients of a compact quantum group

**6**

**1**answer

### Finite compact quantum groups

**5**

**1**answer

### Relating different constructions of the universal compact quantum group

**3**

**0**answers

### Galois descent of a Hopf algebra

**4**

**1**answer

### Non-cosemisimple duals of pointed Hopf algebras

**5**

**1**answer

### Invertible elements of the Hopf algebra quantum $SU(2)$

**0**

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### Hopf algebra antipodes and right left comodule equivalences

**1**

**1**answer

### Example of a sub-bialgebra of a Hopf algebra that is not a Hopf subalgebra

**3**

**0**answers

### Is the category of Yetter-Drinfeld modules abelian?

**7**

**0**answers

### Conceptual proof of braid group actions on quantum groups

**7**

**0**answers

### Are there attempts to numerically finding algebraic structures over finite-dimensional vector spaces?

**4**

**1**answer

### What is the difference between the Yang--Baxter equation and the quantum Yang--Baxter equation?

**2**

**1**answer

### Peter-Weyl theorem (compact quantum groups)

**0**

**1**answer

### Direct sum of representations of a compact quantum group

**0**

**1**answer

### Definition intertwiner of representations of compact quantum groups

**2**

**2**answers

### Kernel of intertwiner is invariant (compact quantum groups)

**4**

**1**answer

### Constructing intertwiners between representations of compact quantum groups

**2**

**1**answer

### Extending $*$-morphisms to the multiplier algebras

**3**

**2**answers

### Convolution of functionals on compact quantum group

**4**

**0**answers

### Are the finite quantum permutation groups, weakly group-theoretical?

**3**

**0**answers

### Where can I find Drinfeld's original papers on quantum groups?

**2**

**0**answers