Compatible, split and family Loday-algebras

2022/02/28 by Das, Apurba
#16E40 #16S80 #17A30 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2202.13682

Abstract

Given a nonsymmetric operad O, we first construct two new nonsymmetric operads O^comp and O^Dend. These operads are respectively useful to study compatible and split Loday-algebras. As an application of the operad O^comp, we show that the cohomology of a compatible associative algebra carries a Gerstenhaber structure. We give an application of the operad O^Dend to dendriform algebras and find generalizations to other Loday-algebras. In the end, we construct another operad Fam(O^Ω)^Dend to study dendriform-family algebras recently introduced in the literature. We also define and study homotopy dendriform-family algebras.

Related

• Deformations of Loday-type algebras and their morphisms
• L_∞-structures and cohomology theory of compatible \mathcal O-operators and compatible dendriform algebras
• Pluriassociative and polydendriform algebras
• Nonabelian Extensions and Factor Systems for the Algebras of Loday
• Cohomology and deformations of dendriform algebras, and Dend_∞-algebras