MODULAR OPERADS AS MODULES OVER THE BRAUER PROPERAD

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...

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Bibliographic Details
Published in:Theory and applications of categories 2022-01, Vol.38 (40), p.1538
Main Author: Stoll, Robin
Format: Article
Language:English
Subjects:
Algebra
Koszul duality
Machinery
Mathematical models
Mathematics
Modular operads
Modules
properads
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Summary: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.
ISSN:1201-561X
1201-561X