Abstract

Lie-Yamaguti color algebras are defined and some examples are provided. It is shown that any Leibniz color algebra has a natural Lie-Yamaguti structure. For a given Lie-Yamaguti color algebra, an enveloping Lie color algebra is constructed and it is proved that any Lie color algebra with reductive decomposition induces a Lie-Yamaguti structure on some of its subspaces.

Keywords: Lie color algebra; Akivis color algebra; Leibniz color algebra; Lie-Yamaguti color algebra.

MSC: 17B55, 17B60, 17B99

Pages:  196$-$206     

Volume  71 ,  Issue  3 ,  2019