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Matched pairs of Lie algebroids

Published online by Cambridge University Press:  18 May 2009

Tahar Mokri
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Sheffield, S3 7RH, England. Email: t.mokri@sheffield.ac.nk
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Abstract

We extend to Lie algebroids the notion variously known as a double Lie algebra (Lu and Weinstein), matched pair of Lie algebras (Majid), or twilled extension of Lie algebras (Kosmann-Schwarzbach and Magri). It is proved that a matched pair of Lie groupoids induces a matched pair of Lie algebroids. Conversely, we show that under certain conditions a matched pair of Lie algebroids integrates to a matched pair of Lie groupoids. The importance of matched pairs of Lie algebroids has been recently demonstrated by Lu.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

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