SUPPORT VARIETIES AND REPRESENTATION TYPE OF SMALL ...

Lusztig's small quantum groups [4, 19] and, more generally, finite dimensional ... small quantum group uq(g) and its Borel-type subalgebra u+ q (g) are wild. This ...

Auslander-Reiten theory for small quantum groups - work in ...

For g = sl2 the small quantum group is the k-algebra with generators E,F,K±1 and relations (R2) KEK−1 = ζ2E. (R3) KFK−1 = ζ−2F. (R4) EF − FE = K−K−1 ζ−ζ−1 ...

Bezrukavnikov, R.; Lachowska, A. The small quantum group and ...

The small quantum group and the Springer resolution. ... Keywords Complex semisimple group; quantum group at a root of unity; small quantum group; tri- ...

Lachowska, Anna On the center of the small quantum group. J ...

Keywords Small quantum group, center, Frobenius algebra, trace, character, simple module, Grothendieck ring, quasi-triangular Hopf algebra, quantum Fourier ...

Chevalley's theorem and quantum groups

Then it is easy to show that uq (sl2) is a Hopf algebra (with the co product inherited from Uq (sl2)). This Hopf algebra is called the small quantum group attached ...

QUANTUM GROUPS, THE LOOP GRASSMANNIAN, AND THE ...

Apr 13, 2004 – let b be the “Borel part” of the “small” quantum group u ⊂ U, and H m. (b, C) the cohomology algebra of b with trivial coefficients. Since b ⊂ U ...

SMALL QUANTUM GROUPS AND THE CLASSIFICATION OF ...

In this paper we apply the theory of the quantum groups Uq(g), and of the small quantum groups uq(g) for q a root of unity, g a semisimple complex Lie algebra ...

On injective modules and support varieties for the small quantum ...

for the small quantum group. Christopher Drupieski. Southeastern Lie Theory Conference on. Homological Methods in Representation Theory. May 23, 2010 ...

COHOMOLOGY FOR QUANTUM GROUPS VIA THE GEOMETRY ...

the small quantum group. When l > h, this cohomology algebra has been calculated by. Ginzburg and Kumar [GK]. Our result requires powerful tools from ...

Triplet and Super Triplet Vertex Algebras, Quantum Groups and ...

Quantum Groups and Modular Forms. Geoff Mason's 60th Birthday ...... is equivalent to the cat- egory of finite-dimensional modules for the small quantum group ...

Pointed Hopf algebras – from enveloping algebras to quantum ...

Group algebras, enveloping algebras of Lie algebras, quantized enveloping algebras, and the small quantum groups of Lusztig are examples of pointed Hopf ...

Quantum Groups and Hopf Algebras

group uq(sU2)(k), which is a finite-dimensional quotient of Uq(sU2)(k) of dimension l3. Finally in Section 4, we show how these small quantum groups and ...

Cohomology of Subregular Tilting Modules for Small Quantum Groups

Let U be a quantum group with divided powers at root of unity constructed from a root. systemR. Letu & U be the small quantum group.The cohomology ofuwith ...

Curriculum Vitae - Columbia University

Thesis “Quantum groups, tensor categories, and knot invariants”. 1998 – 2002 A.B. ... Maui Subfactor Conference Small index subfactors part 3. 2011 Mar.

Pacific Journal of Mathematics

is a semisimple Lie algebra (see [Drinfel'd 1987]), which were found in the mid. 1980s, and by the finite-dimensional small quantum groups uq(g), where q = ϵ is ...

Realizing rings of regular functions via the cohomology of quantum ...

flag variety G/P via the cohomology of the small quantum group. Our main results generalize the important computation of the cohomology ring for the ...

THE SUM OF A FINITE GROUP OF WEIGHTS OF A HOPF ...

groups, (quantum groups over) Lie algebras, the small quantum groups of Lusztig, and their variations .... and is a variation of a small quantum group of Lusztig.

On Injective Modules and Support Varieties for the Small Quantum ...

Sep 4, 2010 – Let uζ (g) be the small quantum group at a root of unity associated to a simple .... extended to results for the entire small quantum group uζ (g).

RESEARCH SUMMARY My research deals with quantum groups ...

by S GELAKI

CATEGORY O FOR QUANTUM GROUPS 1. Introduction Let g ...

induced Hopf algebra structure. 2.2. The small quantum group. We also have the small quantum group uq ⊂ Uq, defined as the subalgebra of Uq generated by ...