2022/12/06 by Shuai Hou, Hou, Shuai, Meiyan Hu +5
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2212.02729
openalex publication_date 2022/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, first we give the notion of a crossed homomorphism on a 3-Lie algebra with respect to an action on another 3-Lie algebra, and characterize it using a homomorphism from a Lie algebra to the semidirect product Lie algebra. We also establish the relationship between crossed homomorphisms and relative Rota-Baxter operators of weight 1 on 3-Lie algebras. Next we construct a cohomology theory for a crossed homomorphism on 3-Lie algebras and classify infinitesimal deformations of crossed homomorphisms using the second cohomology group. Finally, using the higher derived brackets, we construct an L_∞-algebra whose Maurer-Cartan elements are crossed homomorphisms. Consequently, we obtain the twisted L_∞-algebra that controls deformations of a given crossed homomorphism on 3-Lie algebras.