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Integrating morphisms of Lie 2-algebras

Part of: Categories with structure Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  04 February 2013

Behrang Noohi
Behrang Noohi*
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK (email: noohi@maths.qmul.ac.uk)
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Abstract

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Given two Lie 2-groups, we study the problem of integrating a weak morphism between the corresponding Lie 2-algebras to a weak morphism between the Lie 2-groups. To do so, we develop a theory of butterflies for 2-term L∞-algebras. In particular, we obtain a new description of the bicategory of 2-term L∞-algebras. An interesting observation here is that the role played by 1-connected Lie groups in Lie theory is now played by 2-connected Lie 2-groups. Using butterflies, we also give a functorial construction of 2-connected covers of Lie 2 -groups. Based on our results, we expect that a similar pattern generalizes to Lie n-groups and Lie n-algebras.

Keywords

Lie 2-algebraLie 2-groupLie crossed moduleLie butterflyL∞-algebraconnected cover

MSC classification

Secondary: 17B99: None of the above, but in this section 18D05: Double categories, $2$-categories, bicategories and generalizations
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 2 , February 2013 , pp. 264 - 294
Copyright
© The Author(s) 2013

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