Launois, Stephane (2006) On the automorphism groups of qenveloping algebras of nilpotent Lie algebras. In: From Lie Algebras to Quantum Groups, 2830 June 2006, Dep. Mathematics, Univ. Coimbra. (Full text available)
PDF (On the Automorphism Groups)  
Download (234kB)


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:  28 May 2014 10:57 
Resource URI:  https://kar.kent.ac.uk/id/eprint/3158 (The current URI for this page, for reference purposes) 
 Export to:
 RefWorks
 EPrints3 XML
 BibTeX
 CSV
 Depositors only (login required):
Downloads
Downloads per month over past year