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

Stephane Launois·Samuel A Lopes
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Abstract

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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Stephane Launois, Samuel A Lopes. 2006-06-06. On the Hochschild cohomology and the automorphism group of U_q(sl_4^+). https://arxiv.org/abs/math/0606134

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