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.
CITATION STYLE
Fock, V. V., & Goncharov, A. B. (2006). Algebraic Geometry and Number Theory. Algebraic Geometry and Number Theory (Vol. 253, pp. 27–68). Boston, MA: Birkhäuser Boston. Retrieved from http://www.springerlink.com/index/10.1007/978-0-8176-4532-8
Mendeley helps you to discover research relevant for your work.