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Curved infinity-algebras and their characteristic classes

Lazarev, Andrey and Schedler, Travis (2012) Curved infinity-algebras and their characteristic classes. Journal of Topology, 5 (3). pp. 503-528. ISSN 1753-8416

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Abstract

In this paper, we study a natural extension of Kontsevich's characteristic class construction for A∞- and L∞-algebras to the case of curved algebras. These define homology classes on a variant of his graph homology that allows vertices of valence at least 1. We compute this graph homology, which is governed by star-shaped graphs with odd-valence vertices. We also classify non-trivially curved cyclic A∞- and L∞- algebras over a field up to gauge equivalence, and show that these are essentially reduced to algebras of dimension at most 2 with only even-ary operations. We apply the reasoning to compute stability maps for the homology of Lie algebras of formal vector fields. Finally, we explain a generalization of these results to other types of algebras, using the language of operads. A key observation is that operads governing curved algebras are closely related to the Koszul dual of those governing unital algebras.

Item Type: Article
Journal or Publication Title: Journal of Topology
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 59755
Deposited By: ep_importer_pure
Deposited On: 31 Oct 2012 10:55
Refereed?: Yes
Published?: Published
Last Modified: 10 Apr 2014 00:17
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/59755

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