Universal enveloping algebra of a pair of compatible Lie brackets
Rings and Algebras
2023-09-01 v3
Abstract
Applying the Poincare-Birkhoff-Witt property and the Groebner-Shirshov bases technique, we find the linear basis of the associative universal enveloping algebra in the sense of V. Ginzburg and M. Kapranov of a pair of compatible Lie brackets. We state that the growth rate of this universal enveloping over -dimensional compatible Lie algebra equals .
Keywords
Cite
@article{arxiv.2110.06518,
title = {Universal enveloping algebra of a pair of compatible Lie brackets},
author = {Vsevolod Gubarev},
journal= {arXiv preprint arXiv:2110.06518},
year = {2023}
}
Comments
9 p.; v2: the defining relations of the universal enveloping algebra in the sense of V. Ginzburg and M. Kapranov of a pair of compatible Lie brackets are corrected; v3: Remarks 2 and 3 are added