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On the automorphism groups of q-enveloping algebras of nilpotent Lie algebras

Launois, Stephane (2006) On the automorphism groups of q-enveloping algebras of nilpotent Lie algebras. In: Ed. CIM. 28. pp. 125-143. (KAR id:3158)

Abstract

We investigate the automorphism group of the quantised enveloping algebra U of the positive nilpotent part of certain simple complex Lie algebras g in the case where the deformation parameter q \in \mathbb{C}^* is not a root of unity. Studying its action on the set of minimal primitive ideals of U we compute this group in the cases where g=sl_3 and g=so_5 confirming a Conjecture of Andruskiewitsch and Dumas regarding the automorphism group of U. In the case where g=sl_3, we retrieve the description of the automorphism group of the quantum Heisenberg algebra that was obtained independently by Alev and Dumas, and Caldero. In the case where g=so_5, the automorphism group of U was computed in [16] by using previous results of Andruskiewitsch and Dumas. In this paper, we give a new (simpler) proof of the Conjecture of Andruskiewitsch and Dumas in the case where g=so_5 based both on the original proof and on graded arguments developed in [17] and [18].

Item Type: Conference or workshop item (Paper)
Uncontrolled keywords: Rings and Algebras (math.RA); Quantum Algebra (math.QA); Representation Theory (math.RT)
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Stephane Launois
Date Deposited: 06 Jun 2008 17:02 UTC
Last Modified: 16 Nov 2021 09:41 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/3158 (The current URI for this page, for reference purposes)

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