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- W4313466308 abstract "Let G be a Poisson–Lie group equipped with a left invariant contravariant pseudo-Riemannian metric. There are many ways to lift the Poisson structure on G to the tangent bundle TG of G. In this paper, we induce a left invariant contravariant pseudo-Riemannian metric on the tangent bundle TG, and we express in different cases the contravariant Levi-Civita connection and curvature of TG in terms of the contravariant Levi-Civita connection and the curvature of G. We prove that the space of differential forms Ω*(G) on G is a differential graded Poisson algebra if, and only if, Ω*(TG) is a differential graded Poisson algebra. Moreover, we show that G is a pseudo-Riemannian Poisson–Lie group if, and only if, the Sanchez de Alvarez tangent Poisson–Lie group TG is also a pseudo-Riemannian Poisson–Lie group. Finally, some examples of pseudo-Riemannian tangent Poisson–Lie groups are given." @default.
- W4313466308 created "2023-01-06" @default.
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- W4313466308 date "2023-01-03" @default.
- W4313466308 modified "2023-09-30" @default.
- W4313466308 title "Geometry of Tangent Poisson–Lie Groups" @default.
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- W4313466308 doi "https://doi.org/10.3390/math11010240" @default.
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