On the Hochschild cohomology and the automorphism group of U_q(sl_4^+)

Details On the Hochschild cohomology and the automorphism group of U_q(sl_4^+) On the Hochschild cohomology and the automorphism group of U_q(sl_4^+)

2006-06-06

arxiv.org/abs/math/0606134v1

Mathematics

Quantum Algebra

17 pages

Scientific paper

We compute the automorphism group of the q-enveloping algebra U_q(sl_4^+) 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(sl_4^+).

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