Published February 2013 | Version Published
Journal Article Open

Poisson bialgebras

  • 1. ROR icon California Institute of Technology
  • 2. ROR icon Nankai University

Abstract

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.

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).

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Additional details

Identifiers

Eprint ID
37666
Resolver ID
CaltechAUTHORS:20130328-090317154

Funding

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
NKBRPC
2006CB805905
SRFDP
200800550015
SRFDP
201200 31110022

Dates

Created
2013-04-15
Created from EPrint's datestamp field
Updated
2021-11-09
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