Modular operads as modules over the Brauer properad
Quantum Algebra
2022-12-21 v2 Algebraic Topology
Category Theory
Abstract
We show that modular operads are equivalent to modules over a certain simple properad which we call the Brauer properad. Furthermore, we show that, in this setting, the Feynman transform corresponds to the cobar construction for modules of this kind. To make this precise, we extend the machinery of the bar and cobar constructions relative to a twisting morphism to modules over a general properad. This generalizes the classical case of algebras over an operad and might be of independent interest. As an application, we sketch a Koszul duality theory for modular operads.
Cite
@article{arxiv.2202.02201,
title = {Modular operads as modules over the Brauer properad},
author = {Robin Stoll},
journal= {arXiv preprint arXiv:2202.02201},
year = {2022}
}
Comments
70 pages. Published version. Comments still welcome!