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Symplectic double groupoids over Poisson $ (ax+b)$-groups


Author: Kentaro Mikami
Journal: Trans. Amer. Math. Soc. 324 (1991), 447-463
MSC: Primary 17B65; Secondary 22E65, 58F05
DOI: https://doi.org/10.1090/S0002-9947-1991-1025757-X
MathSciNet review: 1025757
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Abstract: First, we classify all the multiplicative Poisson structures on the $ (ax + b)$-group and determine their dual Poisson Lie groups. Next, we show the existence of symplectic groupoid over the Poisson $ (ax + b)$-group. Finally, by the Hamilton-Jacobi method we construct nontrivial symplectic double groupoids and conclude that for each pair of nondegenerate multiplicative Poisson structures of the $ (ax + b)$-group there exists a symplectic double groupoid.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1991-1025757-X
Keywords: Symplectic groupoid, Poisson Lie group, $ (ax + b)$-group
Article copyright: © Copyright 1991 American Mathematical Society

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