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arXiv · 2408.04033

Cohomology of left-symmetric color algebras

Yin Chen·Runxuan Zhang
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Abstract

We develop a new cohomology theory for finite-dimensional left-symmetric color algebras and their finite-dimensional bimodules, establishing a connection between Lie color cohomology and left-symmetric color cohomology. We prove that the cohomology of a left-symmetric color algebra $A$ with coefficients in a bimodule $V$ can be computed by a lower degree cohomology of the corresponding Lie color algebra with coefficients in Hom$(A,V)$, generalizing a result of Dzhumadil'daev in right-symmetric cohomology. We also explore the varieties of two-dimensional and three-dimensional left-symmetric color algebras.

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Yin Chen, Runxuan Zhang. 2024-08-07. Cohomology of left-symmetric color algebras. https://doi.org/10.1080/00927872.2025.2541932

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