## 21 Citations

### A geometric realization of the center of the small quantum group

- Mathematics
- 2022

. We propose a new geometric model for the center of the small quantum group using the cohomology of certain aﬃne Springer ﬁbers. More precisely, we establish an isomorphism between the equivariant…

### The small quantum group and the Springer resolution

- Mathematics
- 2006

In math.RT/0304173 the derived category of the principal block in modules over the Lusztig quantum algebra at a root of unity is related to the derived category of equivariant coherent sheaves on the…

### The center of small quantum groups I: the principal block in type A

- Mathematics
- 2016

We develop an elementary algebraic method to compute the center of the principal block of a small quantum group associated with a complex semisimple Lie algebra at a root of unity. The exemplary case…

### Modular Group Representations and Fusion in Logarithmic Conformal Field Theories and in the Quantum Group Center

- Mathematics
- 2006

The SL(2, ℤ)-representation π on the center of the restricted quantum group at the primitive 2pth root of unity is shown to be equivalent to the SL(2, ℤ)-representation on the extended characters of…

### A counterpart of the Verlinde algebra for the small quantum group

- Mathematics
- 2001

Let $\bar{Pr}$ denote the ideal spanned by the characters of projective modules in the Grothendieck ring of the category of finite dimensional modules over the small quantum group $u_l$. We show that…

### The center of the small quantum group u_q(sl_3) for l=5: a numerical computation

- Mathematics
- 2016

This is a brief note on a numerical computation of the dimension of the center of the small quantum group u_q(sl_3) at the 5th root of unity. The obtained dimension is 57. Using the description of…

### On certain Hochschild cohomology groups for the small quantum group

- MathematicsJournal of Algebra
- 2022

### Kazhdan-Lusztig-dual quantum group for logarithimic extensions of Virasoro minimal models

- Mathematics
- 2007

We derive and study a quantum group gp,q that is Kazhdan-Lusztig dual to the W-algebra Wp,q of the logarithmic (p,q) conformal field theory model. The algebra Wp,q is generated by two currents W+(z)…

### The center of 𝒰q (𝔫ω)

- Mathematics
- 2018

ABSTRACT Based on [24], we point to a new and very useful direction of approach to a general set of problems. We exemplify it here by obtaining the center of a localization of by the covariant…

## References

SHOWING 1-10 OF 24 REFERENCES

### Mappin class group actions on quantum doubles

- Mathematics
- 1994

We study representations of the mapping class group of the punctured torus on the double of a finite dimensional possibly non-semisimple Hopf algebra that arise in the construction of universal,…

### Braided Groups and Quantum Fourier Transform

- Mathematics
- 1994

Abstract We show that acting on every finite-dimensional factorizable ribbon Hopf algebra H there are invertible operators S , T obeying the modular identities ( S T )3 = λ S 2, where λ is a…

### Tensor products of quantized tilting modules

- Mathematics
- 1992

LetUk denote the quantized enveloping algebra corresponding to a finite dimensional simple complex Lie algebraL. Assume that the quantum parameter is a root of unity ink of order at least the Coxeter…

### Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity

- Mathematics
- 1995

An example of a finite dimensional factorizable ribbon Hopf ℂ-algebra is given by a quotientH=uq(g) of the quantized universal enveloping algebraUq(g) at a root of unityq of odd degree. The mapping…

### On the Center of Quantized Enveloping Algebras

- Mathematics
- 1998

Abstract LetUbe a quasitriangular Hopf algebra. One may use theR-matrix ofUin order to construct scalar invariants of knots. Analogously, Reshetikhin wrote down tangle invariants which take their…

### Representations of quantum algebras

- Mathematics
- 1991

It has been pointed out to us (see the Introduction of [1]) that in Section 5 of the above paper we are implicitly using a non-obvious Mackey type result when we apply the results of Section 4. In…

### Invariants of 3-manifolds via link polynomials and quantum groups

- Mathematics
- 1991

The aim of this paper is to construct new topological invariants of compact oriented 3-manifolds and of framed links in such manifolds. Our invariant of (a link in) a closed oriented 3-manifold is a…

### Finite-dimensional Hopf algebras arising from quantized universal enveloping algebra

- Mathematics
- 1990

0.1. An important role in the theory of modular representations is played by certain finite dimensional Hopf algebras u over Fp (the field with p elements, p = prime). Originally, u was defined…

### Combinatorics of Harish-Chandra modules

- Mathematics
- 1998

These lectures survey recent work on the combinatorics of certain infinite dimensional representations of complex semisimple Lie algebras. Their focus is not on understanding the irreducible objects…

### q-Weyl group and a multiplicative formula for universalR-matrices

- Mathematics
- 1990

We define theq-version of the Weyl group for quantized universal enveloping algebras of simple Lie group and we find explicit multiplicative formulas for the universalR-matrix.