Omni-Lie Color Algebras and Lie Color 2-Algebras

TL;DR

This paper introduces Lie color 2-algebras and 2-term color L-infinity algebras, establishing their categorical equivalence and constructing examples from omni-Lie and Leibniz color algebras.

Contribution

It defines and studies Lie color 2-algebras and 2-term color L-infinity algebras, proving their categorical equivalence and providing explicit constructions and examples.

Findings

Category of Lie color 2-algebras is equivalent to 2-term color L-infinity algebras.

Constructed Lie color 2-algebras from omni-Lie color and Leibniz color algebras.

Provided examples of Z^2_2-graded Lie color 2-algebras.

Abstract

The notions of Lie color 2-algebras and 2-term color L-infty-algebras over a group-graded vector space are introduced and studied. It is proved that the category of Lie color 2-algebras and the category of 2-term color L1-algebras are equivalent. We construct Lie color 2-algebras from omni-Lie color algebras and Leibniz color algebras. Some example of $Z^2_2$ -graded Lie color 2-algebras are given.