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Cluster χ-varieties, amalgamation, and Poisson—Lie groups

  • V. V. Fock
  • A. B. Goncharov
Part of the Progress in Mathematics book series (PM, volume 253)

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.

Keywords

Modulus Space Span Tree Simple Root Poisson Structure Braid Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2006

Authors and Affiliations

  • V. V. Fock
    • 1
  • A. B. Goncharov
    • 2
  1. 1.Institute for Theoretical and Experimental PhysicsMoscowRussia
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA

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