CLASSIFICATION OF Uq (sl2)-MODULE ALGEBRA STRUCTURES ON THE QUANTUM PLANE
نویسنده
چکیده
We produce a complete list of Uq (sl2)-module algebra structures on the quantum plane. The (uncountable family of) isomorphism classes of such structures are described. The composition series of representations in question are presented.
منابع مشابه
2 00 5 The quantum algebra U q ( sl 2 ) and its equitable presentation ∗
We show that the quantum algebra Uq(sl2) has a presentation with generators x±1, y, z and relations xx−1 = x−1x = 1, qxy − q−1yx q − q−1 = 1, qyz − q−1zy q − q−1 = 1, qzx − q−1xz q − q−1 = 1. We call this the equitable presentation. We show that y (resp. z) is not invertible in Uq(sl2) by displaying an infinite dimensional Uq(sl2)-module that contains a nonzero null vector for y (resp. z). We c...
متن کاملEf − Fe =
Let Uq(sl2) be the quantized enveloping algebra associated to the simple Lie algebra sl2. In this paper, we study the quantum double Dq of the Borel subalgebra Uq((sl2) ) of Uq(sl2). We construct an analogue of Kostant–Lusztig Z[v, v]-form for Dq and show that it is a Hopf subalgebra. We prove that, over an algebraically closed field, every simple Dq-module is the pullback of a simple Uq(sl2)-m...
متن کاملIrreducible modules for the quantum affine algebra Uq( ̂ sl2) and its Borel subalgebra Uq( ̂ sl2) ≥0
Let Uq(ŝl2) ≥0 denote the Borel subalgebra of the quantum affine algebra Uq(ŝl2). We show that the following hold for any choice of scalars ε0, ε1 from the set {1,−1}. (i) Let V be a finite-dimensional irreducible Uq(ŝl2) -module of type (ε0, ε1). Then the action of Uq(ŝl2) ≥0 on V extends uniquely to an action of Uq(ŝl2) on V . The resulting Uq(ŝl2)-module structure on V is irreducible and of ...
متن کاملAlgebraic Aspects of the Quantum Yang–Baxter Equation
In this paper we examine a variety of algebraic contexts in which the quantum Yang–Baxter equation arises, and derive methods for generating new solutions from given ones. The solutions we describe are encoded in objects which have a module and a comodule structure over a bialgebra. Our work here is based in part on the ideas of [DR1, DR2]. Suppose that R : M ⊗M −→ M ⊗M is a solution to the qua...
متن کاملAn Algebra Associated with a Flag in a Subspace Lattice over a Finite Field and the Quantum Affine Algebra Uq(ŝl2)
In this paper, we introduce an algebra H from a subspace lattice with respect to a fixed flag which contains its incidence algebra as a proper subalgebra. We then establish a relation between the algebra H and the quantum affine algebra Uq1/2(ŝl2), where q denotes the cardinality of the base field. It is an extension of the well-known relation between the incidence algebra of a subspace lattice...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009