# 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
• 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
• 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
• 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
• B. L. FeiginA. M. Semikhatov
• 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
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
• 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
• 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)
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

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,
• 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
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
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
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
• 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
• 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
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
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
• 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.