A differential U-module algebra for U = Ū q sℓ(2) at an even root of unity
نویسندگان
چکیده
منابع مشابه
The nonstandard deformation U ′ q(son) for q a root of unity, Methods of Funct. Anal. Topology 6
We describe properties of the nonstandard q-deformation U ′ q (son) of the universal enveloping algebra U (son) of the Lie algebra son which does not coincide with the Drinfeld–Jimbo quantum algebra Uq(son). In particular, it is shown that there exists an isomorphism from U ′ q (son) to Uq(sln) and that finite dimensional ir-reducible representations of U ′ q (son) separate elements of this alg...
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We study the nonstandard q-deformation U ′ q (so 4) of the universal enveloping algebra U (so 4) obtained by deforming the defining relations for skew-symmetric generators of U (so 4). This algebra is used in quantum gravity and algebraic topology. We construct a homomor-phism φ of U ′ q (so 4) to the certain nontrivial extension of the Drinfeld–Jimbo quantum algebra U q (sl 2) ⊗2 and show that...
متن کاملOn the Center of q - Deformed Algebra U ′ q ( so 3 ) Related to Quantum Gravity at q a Root of 1
It is known that Fairlie–Odesskii algebra U ′ q(so3) appears as algebra of observables in quantum gravity in (2 + 1)-dimensional de Sitter space with space being torus. In this paper, we study the center of this algebra at q a root of 1. It turns out that Casimir elements in this case are algebraically dependent. Using realization of the algebra U ′ q(so3) in terms of quantized lengths of geode...
متن کاملITP-97-9E q-alg/9709035 REPRESENTATIONS OF THE q-DEFORMED ALGEBRA U ′ q(so2,2)
The main aim of this paper is to give classes of irreducible infinite dimensional representations and of irreducible *-representations of the q-deformed algebra U ′ q (so 2,2) which is a real form of the non-standard deformation U ′ q (so 4) of the universal enveloping algebra U (so(4, C)). These representations are described by two complex parameters and are obtained by " analytical continuati...
متن کاملON IRREDUCIBLE WEIGHT REPRESENTATIONS OF A NEW DEFORMATION Uq(sl2) OF U(sl2)
Starting from a Hecke R−matrix, Jing and Zhang constructed a new deformation Uq(sl2) of U(sl2), and studied its finite dimensional representations in [6]. Especically, this algebra is proved to be just a bialgebra, and all finite dimensional irreducible representations are constructed in [6]. In addition, an example is given to show that not every finite dimensional representation of this algeb...
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ژورنال
عنوان ژورنال: Theoretical and Mathematical Physics
سال: 2009
ISSN: 0040-5779,1573-9333
DOI: 10.1007/s11232-009-0035-1