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Integrating -algebras

Part of: Infinite-dimensional manifolds Applied homological algebra and category theory Global differential geometry

Published online by Cambridge University Press:  01 July 2008

André Henriques
André Henriques*
Affiliation:
Mathematisch Instituut, Universiteit Utrecht, PO Box 80.010 NL-3508, TA Utrecht, The Netherlands (email: [email protected])
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Abstract

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Given a Lie n-algebra, we provide an explicit construction of its integrating Lie n-group. This extends work done by Getzler in the case of nilpotent -algebras. When applied to an ordinary Lie algebra, our construction yields the simplicial classifying space of the corresponding simply connected Lie group. In the case of the string Lie 2-algebra of Baez and Crans, we obtain the simplicial nerve of their model of the string group.

Keywords

L_\infty-algebrasimplicial manifoldstring groupLie 2-groupLie 2-algebraKan condition

MSC classification

Secondary: 53C05: Connections, general theory 55U10: Simplicial sets and complexes 58B10: Differentiability questions
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 4 , July 2008 , pp. 1017 - 1045
Copyright
Copyright © Foundation Compositio Mathematica 2008