Abstract
By applying the Poincaré—Birkhoff—Witt property and the Gröbner—Shirshov bases technique, we find the linear basis of the associative universal enveloping algebra in the sense of Ginzburg and Kapranov of a pair of compatible Lie brackets. We state that the growth rate of this universal enveloping over [Formula: see text]-dimensional compatible Lie algebra equals [Formula: see text].
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