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Integrating L∞-algebras

Abstract:

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 L∞-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.

Publication status:
Published
Peer review status:
Peer reviewed
Version:
Author's Original

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Publisher copy:
10.1112/S0010437X07003405

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Publisher:
Cambridge University Press Publisher's website
Journal:
Compositio Mathematica Journal website
Volume:
144
Issue:
4
Pages:
1017-1045
Publication date:
2008-07-01
Acceptance date:
2007-11-24
DOI:
EISSN:
1570-5846
ISSN:
0010-437X
Pubs id:
pubs:693826
URN:
uri:1b553eb9-e300-437b-be81-bc0222e3ab6d
UUID:
uuid:1b553eb9-e300-437b-be81-bc0222e3ab6d
Local pid:
pubs:693826
Keywords:

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