2024/08/07 by Yin Chen, Runxuan Zhang, Chen, Yin +1
Mathematics · #Advanced Topics in Algebra #Rings, Modules, and Algebras #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2408.04033
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.