On the center of the small quantum group

@article{Lachowska2001OnTC,
  title={On the center of the small quantum group},
  author={Anna Lachowska},
  journal={Journal of Algebra},
  year={2001},
  volume={262},
  pages={313-331}
}
  • A. Lachowska
  • Published 13 July 2001
  • Mathematics
  • Journal of Algebra

A geometric realization of the center of the small quantum group

. 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

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

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

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

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

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

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

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)

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

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

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

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

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

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

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

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

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

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

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.