Generalized lie bialgebras
作者:
Tan Youjun,
Zhang-Ju Liu,
期刊:
Communications in Algebra
(Taylor Available online 1998)
卷期:
Volume 26,
issue 7
页码: 2293-2319
ISSN:0092-7872
年代: 1998
DOI:10.1080/00927879808826277
出版商: Gordon and Breach Science Publishers Ltd.
数据来源: Taylor
摘要:
We generalize Lie bialgebras and Lie bialgebioids to new objects which we call generalized Lie bialgebras. Similar to Lie bialgebras and Lie bial-gebroids, generalized Lie bialgebras are self-dual and generate canonically Hamiltonian structures on their representative spaces. We show that for a generalized Lie bialgebra (E, Ē), a pair (L1,L2) ofE+Ē is again a generalized Lie bialgebra iff (L1,L2) is a Dirac structure pair . Construction of generalized Lie bialgebras by using Poisson tensors and Hamiltonian operators are also discussed in detail and an example relating to an infinite-dimensional integrable system is given.
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