2015/09/18 by A. Cesaro, Cesaro, Andrea
Mathematics · #18D50 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1509.05599
openalex publication_date 2015/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study an analogue of the notion of p-restricted Lie-algebra and of the notion of divided power algebra for PreLie-algebras. We deduce our definitions from the general theory of operads. We consider two variants Λ(P,-) and Γ(P,-) of the monad S(P,-) which governs the category of algebras classically associated to an operad P. For the operad of PreLie-algebras P=PreLie, we prove that the category of algebras over the monad Λ(PreLie,-) is identified with an already defined category of p-restricted PreLie-algebras introduced by A. Dzhumadil'daev. We give an explicit description of the structure an algebra over the monad Γ(PreLie,-) in terms of brace-type operations and we compute the relations between these generating operations. We prove that classical examples of PreLie-algebras occurring in deformation theory actually form Γ(PreLie,-)-algebras.