Some remarks on quantized Lie superalgebras of classical type
| Venue: | Preprint. LINK INVARIANTS FROM LIE SUPERALGEBRAS 23 |
| Citations: | 4 - 4 self |
BibTeX
@INPROCEEDINGS{Geer_someremarks,
author = {Nathan Geer},
title = {Some remarks on quantized Lie superalgebras of classical type},
booktitle = {Preprint. LINK INVARIANTS FROM LIE SUPERALGEBRAS 23},
year = {}
}
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Abstract
Abstract. In this paper we use the Etingof-Kazhdan quantization of Lie bisuperalgebras 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. 1.
