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

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dc.creatorLaunois, S.
dc.date2007-12-03
dc.date.accessioned2026-07-07T08:46:54Z
dc.date.available2026-07-07T08:46:54Z
dc.descriptionWe 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].
dc.description19p
dc.identifierhttps://arxiv.org/abs/0712.0282
dc.identifierhttp://arxiv.org/abs/0712.0282
dc.identifierProc. workshop "From Lie Algebras to Quantum Groups", Ed. CIM, vol. 28 (2007), 125-143
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/143412
dc.subjectRings and Algebras
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.titleOn the automorphism groups of q-enveloping algebras of nilpotent Lie algebras
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