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Abstract
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In this paper, we obtain the classical r-matrices of real two- and three-dimensional
Jacobi–Lie bialgebras. In this way, we classify all non-isomorphic real two- and threedimensional
coboundary Jacobi–Lie bialgebras and their types (triangular and quasitriangular).
Also, we obtain the generalized Sklyanin bracket formula by use of which,
we calculate the Jacobi structures on the related Jacobi–Lie groups. Finally, we present
a new method for constructing classical integrable systems using coboundary Jacobi–Lie
bialgebras.
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