Integration of semidirect product Lie 2-algebras (Q2920430)
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scientific article; zbMATH DE number 6094233
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Integration of semidirect product Lie 2-algebras |
scientific article; zbMATH DE number 6094233 |
Statements
16 October 2012
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Representation up to homotopy
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\(L_\infty\)-algebras
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Lie 2-algebras
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\(\langle\) omni-Lie algebras
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crossed modules
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integration
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butterfly
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0.94171154
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0.93753994
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0.92962074
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0.9094259
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0.9040311
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0.9026049
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Integration of semidirect product Lie 2-algebras (English)
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In recent years people have paid much intention to the integration of Lie algebras. Here ''integration'' is meant in the same sense in which a Lie algebra is integrated to a corresponding Lie group. In this paper, the semidirect product of a Lie algebra and a 2-representation up to homotopy is a Lie 2-algebra. Such Lie 2-algebras include many examples arising from the Courant algebroid appearing in generalized complex geometry. In this paper, one integrates such Lie 2-algebra to a strict Lie 2-group in the finite-dimensional case. Finally one concludes the paper by giving the integration of omni-Lie algebras as an application.
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