The Cohomology of Algebras over Moduli Spaces
Takashi Kimura (University of North Carolina), Alexander A. Voronov, (University of Pennsylvania)
TL;DR
This paper introduces a cohomology theory for algebras over moduli space operads, providing new invariants for conformal field theories and vertex operator algebras, including their infinitesimal deformations.
Contribution
It develops a novel cohomology framework for algebras over moduli space operads, linking algebraic structures to geometric invariants.
Findings
Defines cohomology for algebras over moduli space operads
Identifies invariants of conformal field theories and vertex operator algebras
Characterizes infinitesimal deformations of these algebras
Abstract
The purpose of this paper is to introduce the cohomology of various algebras over an operad of moduli spaces including the cohomology of conformal field theories (CFT's) and vertex operator algebras (VOA's). This cohomology theory produces a number of invariants of CFT's and VOA's, one of which is the space of their infinitesimal deformations.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Rings, Modules, and Algebras