4 papers · 1 filter
Cyclic operads, Koszul complexes, and hairy graph complexes
Geoffrey Powell
In this paper, we revisit the construction of the hairy graph complexes associated to a cyclic operad, by exploiting modules over the appropriate twisted linearization of the downw…
Lie algebra homology with coefficients tensor products of the adjoint representation in relative polynomial degree 2
Geoffrey Powell
The homology of free Lie algebras with coefficients in tensor products of the adjoint representation working over Q contains important information on the homological properties of…
Relative nonhomogeneous Koszul duality for PROPs associated to nonaugmented operads
Geoffrey Powell
The purpose of this paper is to show how Positselski's relative nonhomogeneous Koszul duality theory applies when studying the linear category underlying the PROP associated to a (…
On fundamental structure underlying Lie algebra homology with coefficients tensor products of the adjoint representation
Geoffrey Powell
This paper exhibits fundamental structure underlying Lie algebra homology with coefficients in tensor products of the adjoint representation, mostly focusing upon the case of free…