# Primitive ideals and automorphism group of Uq+(B2)

Launois, Stephane (2007) Primitive ideals and automorphism group of Uq+(B2). Journal of Algebra and its Applications, 6 (1). pp. 21-47. ISSN 0219-4988. (KAR id:3155)

 PDF (Primitive Ideals and Automorphism Group ) Language: English Download (346kB) Preview Preview This file may not be suitable for users of assistive technology. Request an accessible format

## Abstract

Let g be a complex simple Lie algebra of type B-2 and q be a nonzero complex number which is not a root of unity. In the classical case, a theorem of Dixmier asserts that the simple factor algebras of Gelfand-Kirillov dimension 2 of the positive part U+(g) of the enveloping algebra of g are isomorphic to the first Weyl algebra. In order to obtain some new quantized analogues of the first Weyl algebra, we explicitly describe the prime and primitive spectra of the positive part U+ q (g) of the quantized enveloping algebra of g and then we study the simple factor algebras of Gelfand-Kirillov dimension 2 of U+ q (g). In particular, we show that the centers of such simple factor algebras are reduced to the ground field C and we compute their group of invertible elements. These computations allow us to prove that the automorphism group of U-q(+) (g) is isomorphic to the torus (C*)(2), as conjectured by Andruskiewitsch and Dumas.

Item Type: Article quantized enveloping algebra; Weyl algebra; primitive ideals; automorphisms Q Science > QA Mathematics (inc Computing science) Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Stephane Launois 03 Jun 2008 14:37 UTC 16 Feb 2021 12:15 UTC https://kar.kent.ac.uk/id/eprint/3155 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-7252-8515