Lie-Yamaguti Algebra Bundle

TL;DR

This paper introduces Lie-Yamaguti algebra bundles, develops their cohomology theory, and explores their abelian extensions, motivated by geometric considerations and providing a new mathematical framework.

Contribution

It defines Lie-Yamaguti algebra bundles, establishes their cohomology groups, and studies abelian extensions, connecting geometric origins with algebraic structures.

Findings

Defined Lie-Yamaguti algebra bundles

Developed cohomology groups for these bundles

Analyzed abelian extensions and their cohomological classification

Abstract

We introduce the notion of Lie-Yamaguti algebra bundle, define its cohomology groups with coefficients in a representation and show that such bundles appeared naturally from geometric considerations in the work of M. Kikkawa, which motivates us to introduce this object in the proper mathematical framework. We also study abelian extensions of Lie-Yamaguti algebra bundles and investigate their relationship with suitable cohomology group.