Zobrazeno 1 - 10
of 136
pro vyhledávání: '"Powell, Geoffrey"'
Autor:
Powell, Geoffrey
A filtration of the morphisms of the $k$-linearization $k \mathbf{FS}$ of the category $\mathbf{FS}$ of finite sets and surjections is constructed using a natural $k \mathbf{FI}^{op}$-module structure induced by restriction, where $\mathbf{FI}$ is th
Externí odkaz:
http://arxiv.org/abs/2407.11627
Autor:
Powell, Geoffrey
We study the structure of the category of representations of $\mathbf{FA}$, the category of finite sets and all maps, mostly working over a field of characteristic zero. This category is not semi-simple and exhibits interesting features. We first con
Externí odkaz:
http://arxiv.org/abs/2407.11623
Autor:
Powell, Geoffrey
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 (non-augmented) operad of a certain form, in particular assuming that t
Externí odkaz:
http://arxiv.org/abs/2406.08132
Autor:
Powell, Geoffrey
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 Lie algebras. The main result yields a DG category that is constructed
Externí odkaz:
http://arxiv.org/abs/2309.07607
Autor:
Powell, Geoffrey
The author has shown that the category of analytic contravariant functors on $\mathbf{gr}$, the category of finitely-generated free groups, is equivalent to the category of left modules over the PROP associated to the Lie operad, working over $\mathb
Externí odkaz:
http://arxiv.org/abs/2309.07605
Autor:
Powell, Geoffrey
This paper is motivated by the study of Turchin and Willwacher's bead representations. The problem is reformulated here in terms of the Lie algebra homology of a free Lie algebra with coefficients in tensor products of the adjoint representation. The
Externí odkaz:
http://arxiv.org/abs/2209.08970
Autor:
Powell, Geoffrey
The purpose of this paper is to give information on the FI-homology of the standard injective cogenerators of the category of FI-modules, where FI is the category of finite sets and injections. Working over a field k of characteristic zero, a full ca
Externí odkaz:
http://arxiv.org/abs/2209.08963