Some Remarks on Quantized Lie Superalgebras of Classical Type
نویسنده
چکیده
In this paper we use the Etingof-Kazhdan quantization of Lie bisuperalgebras to investigate some interesting questions related to DrinfeldJimbo type superalgebra associated to a Lie superalgebra of classical type. It has been shown that the D-J type superalgebra associated to a Lie superalgebra of type A-G, with the distinguished Cartan matrix, is isomorphic to the E-K quantization of the Lie superalgebra. The first main result in the present paper is to extend this to arbitrary Cartan matrices. This paper also contains two other main results: 1) a theorem stating that all highest weight modules of a Lie superalgebra of type A-G can be deformed to modules over the corresponding D-J type superalgebra and 2) a super version of the Drinfeld-Kohno Theorem.
منابع مشابه
Locally finite basic classical simple Lie superalgebras
In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.
متن کاملOn Defining Relations of the Affine Lie Superalgebras and Their Quantized Universal Enveloping Superalgebras
Introduction. In this paper, we give defining relations of the affine Lie superalgebras and defining relations of a super-version of the Drinfeld[D1]Jimbo[J] affine quantized enveloping algebras. As a result, we can exactly define the affine quantized universal enveloping superalgebras with generators and relations. Moreover we give a Drinfeld’s realization of Uh(ŝl(m|n)). For the Kac-Moody Lie...
متن کاملThe Kontsevich integral and quantized Lie superalgebras
Given a finite dimensional representation of a semisimple Lie algebra there are two ways of constructing link invariants: 1) quantum group invariants using the R-matrix, 2) the Kontsevich universal link invariant followed by the Lie algebra based weight system. Le and Murakami showed that these two link invariants are the same. These constructions can be generalized to some classes of Lie super...
متن کاملUniversal Central Extension of Current Superalgebras
Representation as well as central extension are two of the most important concepts in the theory of Lie (super)algebras. Apart from the interest of mathematicians, the attention of physicist are also drawn to these two subjects because of the significant amount of their applications in Physics. In fact for physicists, the study of projective representations of Lie (super)algebras are very impo...
متن کاملOn generalized reduced representations of restricted Lie superalgebras in prime characteristic
Let $mathbb{F}$ be an algebraically closed field of prime characteristic $p>2$ and $(g, [p])$ a finite-dimensional restricted Lie superalgebra over $mathbb{F}$. It is showed that anyfinite-dimensional indecomposable $g$-module is a module for a finite-dimensional quotient of the universal enveloping superalgebra of $g$. These quotient superalgebras are called the generalized reduced enveloping ...
متن کامل