In this paper, the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free involutive hom-associative color algebra on a hom-module is described and applied to obtain the universal enveloping algebra of an involutive hom-Lie color algebra. Finally, the construction is applied to obtain the well-known Poincaré-Birkhoff-Witt theorem for Lie algebras to the enveloping algebra of an involutive color hom-Lie algebra.
ARMAKAN, ABDOREZA; SILVESTROV, SERGEI; and FARHANGDOOST, MOHAMMAD REZA
"Enveloping algebras of color hom-Lie algebras,"
Turkish Journal of Mathematics: Vol. 43:
1, Article 26.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss1/26