Abstract
In this paper, starting from a split semisimple real Lie group G with trivial center, we define a family of varieties with additional structures. We describe them as cluster χ-varieties, as defined in [FG2]. In particular they are Poisson varieties. We define canonical Poisson maps of these varieties to the group G equipped with the standard Poisson—Lie structure defined by V. Drinfeld in [D, D1]. One of them maps to the group birationally and thus provides G with canonical rational coordinates.
To Vladimir Drinfeld for his 50th birthday.
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Fock, V.V., Goncharov, A.B. (2006). Cluster χ-varieties, amalgamation, and Poisson—Lie groups. In: Ginzburg, V. (eds) Algebraic Geometry and Number Theory. Progress in Mathematics, vol 253. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4532-8_2
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DOI: https://doi.org/10.1007/978-0-8176-4532-8_2
Publisher Name: Birkhäuser Boston
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