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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2012.01561 |
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Table of Contents:
- This paper develops a cohomology theory for Hom-Leibniz algebras using the $β$-Nijenhuis--Richardson bracket and applies it to classify non-abelian extensions. We introduce left, and right versions of the bracket, each defining a graded Lie algebra structure on the space of $β$-cochains. The main result establishes that equivalence classes of split extensions of a Hom-Leibniz algebra $L$ by $V$ are in bijection with the second cohomology space $H^2(L,V)$, generalizing classical results from Lie and Leibniz algebra theory. We characterize extensions explicitly through 2-cocycles $(λ_l, λ_r, θ)$ and provide complete classifications of low-dimensional cases.