2024/09/08 by Jiang, Jun, Sheng, Yunhe, Sun, Geyi
#FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2409.05041
In this paper, first we use the higher derived brackets to construct an L_∞-algebra, whose Maurer-Cartan elements are 3-Lie algebra morphisms. Using the differential in the L_∞-algebra that govern deformations of the morphism, we give the cohomology of a 3-Lie algebra morphism. Then we study the rigidity and stability of 3-Lie algebra morphisms using the established cohomology theory. In particular, we show that if the first cohomology group is trivial, then the morphism is rigid; if the second cohomology group is trivial, then the morphism is stable. Finally, we study the stability of 3-Lie subalgebras similarly.