On the Hochschild cohomology and the automorphism group of U_q(sl₄⁺)

2006/06/06 by Stéphane Launois, Stephane Launois, Launois, Stephane +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.QA #math.RA #msc:16E40 #msc:16W20 #msc:16W25 #msc:17B37

paper · pdf · doi:10.48550/arxiv.math/0606134

17 pages

arxiv created 2006/06/06 · arxiv updated 2009/12/01

Abstract

We compute the automorphism group of the q-enveloping algebra U_q(sl₄⁺) of the nilpotent Lie algebra of strictly upper triangular matrices of size 4. The result obtained gives a positive answer to a conjecture of Andruskiewitsch and Dumas. We also compute the derivations of this algebra and then show that the Hochschild cohomology group of degree 1 of this algebra is a free (left)-module of rank 3 (which is the rank of the Lie algebra sl(4)) over the center of U_q(sl₄⁺).

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