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Feynman diagrams and minimal models for operadic algebras

Chuang, J. and Lazarev, A. (2010). Feynman diagrams and minimal models for operadic algebras. Journal of the London Mathematical Society, 81(2), pp. 317-337. doi: 10.1112/jlms/jdp073

Abstract

We construct an explicit minimal model for an algebra over the cobar-construction of a differential graded operad. The structure maps of this minimal model are expressed in terms of sums over decorated trees. We introduce the appropriate notion of a homotopy equivalence of operadic algebras and show that our minimal model is homotopy equivalent to the original algebra. All this generalizes and gives a conceptual explanation of well-known results for A∞-algebras. Furthermore, we show that these results carry over to the case of algebras over modular operads; the sums over trees get replaced by sums over general Feynman graphs. As a by-product of our work we prove gauge-independence of Kontsevich's ‘dual construction’ producing graph cohomology classes from contractible differential graded Frobenius algebras.

Publication Type: Article
Publisher Keywords: STRING FIELD-THEORY, HOMOTOPY ALGEBRAS
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/187
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