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Feynman diagrams and minimal models for operadic algebras.

Chuang, Joseph and Lazarev, Andrey (2010) Feynman diagrams and minimal models for operadic algebras. Journal of the London Mathematical Society, 81 (2). pp. 317-337.

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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.

Item Type: Article
Journal or Publication Title: Journal of the London Mathematical Society
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 59751
Deposited By: ep_importer_pure
Deposited On: 02 Nov 2012 14:00
Refereed?: Yes
Published?: Published
Last Modified: 10 Apr 2014 00:17
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/59751

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