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arXiv · 2110.06518

Universal enveloping algebra of a pair of compatible Lie brackets

Vsevolod Gubarev
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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 $n$-dimensional compatible Lie algebra equals $n+1$.

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Vsevolod Gubarev. 2021-10-13. Universal enveloping algebra of a pair of compatible Lie brackets. https://doi.org/10.1142/s0218196722500588

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