2022/02/07 by Apurba Das, Das, Apurba · 1 citation
Mathematics · #16S80 #17A32 #17A99 #17B56 #18G55 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16S80 #msc:17A32 #msc:17A99 #msc:17B56 #msc:18G55
paper · pdf · doi:10.48550/arxiv.2202.03160
16 pages
arxiv created 2022/02/07 · arxiv updated 2022/02/08
The notion of pre-Leibniz algebras was recently introduced in the study of Rota-Baxter operators on Leibniz algebras. In this paper, we first construct a graded Lie algebra whose Maurer-Cartan elements are pre-Leibniz algebras. Using this characterization, we define the cohomology of a pre-Leibniz algebra with coefficients in a representation. This cohomology is shown to split the Loday-Pirashvili cohomology of Leibniz algebras. As applications of our cohomology, we study formal and finite order deformations of a pre-Leibniz algebra. Finally, we define homotopy pre-Leibniz algebras and classify some special types of homotopy pre-Leibniz algebras.