2020/02/24 by Dotsenko, Vladimir, Foissy, Loïc
#05C05 #16D40 #17B35 (Secondary) #18D50 (Primary) #Category Theory (math.CT) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2002.10536
In this paper, we study the C-enriched pre-Lie operad defined by Calaque and Willwacher for any Hopf cooperad C to produce conceptual constructions of the operads acting on various deformation complexes. Maps between Hopf cooperads lead to maps between the corresponding enriched pre-Lie operads; we prove criteria for the module action of the domain on the codomain to be free, on the left and on the right. In particular, this implies a new functorial Poincaré--Birkhoff--Witt type theorem for universal enveloping brace algebras of pre-Lie algebras.