2024/11/15 by Yin Chen, Runxuan Zhang, Chen, Yin +1
Mathematics · #17B75 #17D25 #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2411.10370
openalex publication_date 2024/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.