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

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

2007-12-03

arxiv.org/abs/0712.0282v1

Proc. workshop "From Lie Algebras to Quantum Groups", Ed. CIM, vol. 28 (2007), 125-143

Mathematics

Rings and Algebras

19p

Scientific paper

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].

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