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Poisson bialgebras

Ni, Xiang and Bai, Chengming (2013) Poisson bialgebras. Journal of Mathematical Physics, 54 (2). Art. No. 023515. ISSN 0022-2488.

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We introduce a notion of Poisson bialgebra as an analogue of a Lie bialgebra of Drinfeld. Poisson bialgebras exhibit many familiar properties of Lie bialgebras. In particular, they can be constructed from a combination of the classical Yang-Baxter equation and the associative Yang-Baxter equation and there exists a natural Drinfeld classical double. Moreover, Poisson bialgebras are related to certain algebraic structures and they fit naturally into a framework to construct compatible Poisson brackets in integrable systems.

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Additional Information:© 2013 American Institute of Physics. Received 25 November 2012; accepted 31 January 2013; published online 28 February 2013. The first author thanks Professor V. N. Zhelyabin for kindly sending his paper to him. This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 10621101, 10920161, 11271202, and 11221091), NKBRPC (Grant No. 2006CB805905), and SRFDP (Grant Nos. 200800550015 and 201200 31110022).
Funding AgencyGrant Number
National Natural Science Foundation of China (NSFC)10621101
National Natural Science Foundation of China (NSFC)10920161
National Natural Science Foundation of China (NSFC)11271202
National Natural Science Foundation of China (NSFC)11221091
SRFDP201200 31110022
Subject Keywords:Lie algebras; Poisson equation
Issue or Number:2
Classification Code:PACS: 02.20.Sv
Record Number:CaltechAUTHORS:20130328-090317154
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Official Citation:Poisson bialgebras Xiang Ni and Chengming Bai, J. Math. Phys. 54, 023515 (2013), DOI:10.1063/1.4792668
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37666
Deposited By: Tony Diaz
Deposited On:15 Apr 2013 19:57
Last Modified:03 Oct 2019 04:49

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