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 . (Full text available)

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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
Uncontrolled keywords: quantized enveloping algebra; Weyl algebra; primitive ideals; automorphisms
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Stephane Launois
Date Deposited: 03 Jun 2008 14:37
Last Modified: 28 May 2014 10:56
Resource URI: http://kar.kent.ac.uk/id/eprint/3155 (The current URI for this page, for reference purposes)
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