Some remarks on quantized Lie superalgebras of classical type

Details Some remarks on quantized Lie superalgebras of classical type Some remarks on quantized Lie superalgebras of classical type

2005-08-23

arxiv.org/abs/math/0508440v2

Mathematics

Quantum Algebra

This version has minor corrections asked for by the referee

Scientific paper

In this paper we use the Etingof-Kazhdan quantization of Lie bi-superalgebras to investigate some interesting questions related to Drinfeld-Jimbo 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.

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