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

Launois, S. (2006) On the automorphism groups of q-enveloping algebras of nilpotent Lie algebras. In: From Lie Algebras to Quantum Groups, 28-30 June 2006, Dep. Mathematics, Univ. Coimbra.

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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:	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:	06 Jun 2008 17:02
Last Modified:	05 Sep 2011 23:31
Resource URI:	http://kar.kent.ac.uk/id/eprint/3158 (The current URI for this page, for reference purposes)

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