The local structure of Lie bialgebroids

Zhang Ju Liu; Ping Xu

doi:10.1023/A:1020218813233

The local structure of Lie bialgebroids

Zhang Ju Liu, Ping Xu

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We study the local structure of Lie bialgebroids at regular points. In particular, we classify all transitive Lie bialgebroids. In special cases, they are connected to classical dynamical r-matrices and matched pairs induced by Poisson group actions.

Original language	English (US)
Pages (from-to)	15-28
Number of pages	14
Journal	Letters in Mathematical Physics
Volume	61
Issue number	1
DOIs	https://doi.org/10.1023/A:1020218813233
State	Published - Jul 2002

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1023/A:1020218813233

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title = "The local structure of Lie bialgebroids",

abstract = "We study the local structure of Lie bialgebroids at regular points. In particular, we classify all transitive Lie bialgebroids. In special cases, they are connected to classical dynamical r-matrices and matched pairs induced by Poisson group actions.",

author = "Liu, {Zhang Ju} and Ping Xu",

note = "Funding Information: $Research partially supported by NSF of China and the Research Project of {\textquoteleft}Nonlinear Science{\textquoteright}. $$Research partially supported by NSF grant DMS00-72171. zThroughout the paper, we adapt the convention that elements in g (or g*) are automatically considered as constant sections on A (or A*) unless otherwise specified.",

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AU - Xu, Ping

N1 - Funding Information: $Research partially supported by NSF of China and the Research Project of ‘Nonlinear Science’. $$Research partially supported by NSF grant DMS00-72171. zThroughout the paper, we adapt the convention that elements in g (or g*) are automatically considered as constant sections on A (or A*) unless otherwise specified.

PY - 2002/7

Y1 - 2002/7

N2 - We study the local structure of Lie bialgebroids at regular points. In particular, we classify all transitive Lie bialgebroids. In special cases, they are connected to classical dynamical r-matrices and matched pairs induced by Poisson group actions.

AB - We study the local structure of Lie bialgebroids at regular points. In particular, we classify all transitive Lie bialgebroids. In special cases, they are connected to classical dynamical r-matrices and matched pairs induced by Poisson group actions.

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The local structure of Lie bialgebroids

Abstract

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