# 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: From Lie Algebras to Quantum Groups, 28-30 June 2006, Dep. Mathematics, Univ. Coimbra. (Full text available)

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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) Rings and Algebras (math.RA); Quantum Algebra (math.QA); Representation Theory (math.RT) Q Science > QA Mathematics (inc Computing science) Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial ScienceFaculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics Stephane Launois 06 Jun 2008 17:02 28 May 2014 10:57 https://kar.kent.ac.uk/id/eprint/3158 (The current URI for this page, for reference purposes)
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