TY - JOUR

T1 - Universal enveloping algebra of a pair of compatible Lie brackets

AU - Gubarev, Vsevolod

N1 - Publisher Copyright: © 2022 World Scientific Publishing Company.

PY - 2022/11/1

Y1 - 2022/11/1

N2 - 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 n-dimensional compatible Lie algebra equals n + 1.

AB - 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 n-dimensional compatible Lie algebra equals n + 1.

KW - compatible Lie brackets

KW - growth rate

KW - Gröbner - Shirshov basis

KW - Universal enveloping algebra over an operad

UR - http://www.scopus.com/inward/record.url?scp=85136237535&partnerID=8YFLogxK

U2 - 10.1142/S0218196722500588

DO - 10.1142/S0218196722500588

M3 - Article

AN - SCOPUS:85136237535

VL - 32

SP - 1335

EP - 1344

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

SN - 0218-1967

IS - 7

ER -