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arXiv · 2411.10370

Deformations of left-symmetric color algebras

Yin Chen·Runxuan Zhang
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Abstract

We develop a deformation theory for finite-dimensional left-symmetric color algebras, which can be used to construct new algebraic structures and interpret left-symmetric color cohomology spaces of lower degrees. We explore equivalence classes and extendability of deformations for a fixed left-symmetric color algebra, demonstrating that each infinitesimal deformation is nontrivially extendable if the third cohomology subspace of degree zero is trivial. We also study Nijenhuis operators and Rota-Baxter operators on a left-symmetric color algebra, providing a better understanding of the equivalence class of the trivial infinitesimal deformation.

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Yin Chen, Runxuan Zhang. 2024-11-15. Deformations of left-symmetric color algebras. https://arxiv.org/abs/2411.10370

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