Related papers: A differential U-module algebra for U=U_q sl(2) at…

We introduce a Kazhdan--Lusztig-dual quantum group for (1,p) Virasoro logarithmic minimal models as the Lusztig limit of the quantum sl(2) at pth root of unity and show that this limit is a Hopf algebra. We calculate tensor products of…

We study the homological properties of Schur algebras $S(p, 2p)$ over a field $k$ of positive characteristic $p$, focusing on their interplay with the representation theory of quotients of group algebras of symmetric groups via Schur-Weyl…

We define nonselfadjoint operator algebras with generators $L_{e_1},..., L_{e_n}, L_{f_1},...,L_{f_m}$ subject to the unitary commutation relations of the form \[ L_{e_i}L_{f_j} = \sum_{k,l} u_{i,j,k,l} L_{f_l}L_{e_k}\] where $u=…

Noncompact forms of the Drinfeld-Jimbo quantum groups U_q(g) with (H_i)* = H_i, (X_i^{+-})* = s_i X_i^{-+} for s_i= +-1 are studied at roots of unity. This covers g = so(n,2p), su(n,p), so*(2l), sp(n,p), sp(l,R), and exceptional cases.…

In this work, we construct the algebra of differential forms with the cube of exterior differential equal to zero on one-dimensional space. We prove that this algebra is a graded q-differential algebra where q is a cubic root of unity.…

In this paper we classify all simple weight modules for a quantum group $U_q$ at a complex root of unity $q$ when the Lie algebra is not of type $G_2$. By a weight module we mean a finitely generated $U_q$-module which has finite…

For quantized universal enveloping algebras we construct weight modules by inducing representations of the centralizer of the Cartan subalgebra in the quantized universal enveloping algebra. The induced modules arising from…

The algebra dual to Woronowicz's deformation of the 2-\-di\-men\-sion\-al Euclidean group is constructed. The same algebra is obtained from $SU_{q}(2)$ via contraction on both the group and algebra levels.

Representations of the quantum superalgebra U_q[osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U_q[osp(1/2)] in which the…

Motivated by recent problems regarding the symmetry of Hecke algebras, we investigate the symmetry of the endomorphism algebra $E_P(M)$ for $P$ a $p$-group and $M$ a $kP$-module with $k$ a field of characteristic $p$. We provide a complete…

Embeddings of the CAR (canonical anticommutation relations) algebra of fermions into the Cuntz algebra ${\cal O}_2$ (or ${\cal O}_{2d}$ more generally) are presented by using recursive constructions. As a typical example, an embedding of…

Let p be prime. A noncommutative p-solenoid is the C*-algebra of Z[1/p] x Z[1/p] twisted by a multiplier of that group, where Z[1/p] is the additive subgroup of the field Q of rational numbers whose denominators are powers of p. In this…

We formulate a precise connection between the new Drinfeld presentation of a quantum affine algebra $U_q\widehat{\mathfrak{g}}$ and the new Drinfeld presentation of affine coideal subalgebras of split type recently discovered by Lu and…

Based on our previous work on the recursive fermion system in the Cuntz algebra, it is shown that a nonlinear transformation group of the CAR fermion algebra is induced from a $U(2^p)$ action on the Cuntz algebra ${\cal O}_{2^p}$ with an…

The factorization of the universal R-matrix corresponding to so called Drinfeld Hopf structure is described on the example of quantum affine algebra $U_q(\hat{sl}_2)$. As a result of factorization procedure we deduce certain differential…

We define a natural quantum analogue for the ${\cal Z}$ algebra, and which we refer to as the ${\cal Z}_q$ algebra, by modding out the Heisenberg algebra from the quantum affine algebra $U_q(\hat{sl(2)})$ with level $k$. We discuss the…

After reviewing the recent results on the Drinfeld realization of the face type elliptic quantum group B_{q,lambda}(sl_N^) by the elliptic algebra U_{q,p}(sl_N^), we investigate a fusion of the vertex operators of U_{q,p}(sl_N^). The basic…

We introduce an elliptic algebra $U_{q,p}(\hat{sl_2})$ with $p=q^{2r} (r\in \R_{>0})$ and present its free boson representation at generic level $k$. We show that this algebra governs a structure of the space of states in the $k-$fusion…

The quantum affine $\CU_q (\hat{sl(2)}) $ symmetry is studied when $q^2$ is an even root of unity. The structure of this algebra allows a natural generalization of N=2 supersymmetry algebra. In particular it is found that the momentum…

Let M and N be even-dimensional oriented real manifolds, and $u:M \to N$ be a smooth mapping. A pair of complex structures at M and N is called u-compatible if the mapping u is holomorphic with respect to these structures. The quotient of…