Lie-Yamaguti Algebra Bundle
Saikat Goswami, Goutam Mukherjee

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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models
