Affordable Access

Cluster structures on simple complex Lie groups and the Belavin-Drinfeld classification

Authors
  • Gekhtman, Michael
  • Shapiro, Michael
  • Vainshtein, Alek
Type
Published Article
Publication Date
Mar 25, 2011
Submission Date
Dec 29, 2010
Source
arXiv
License
Yellow
External links

Abstract

We study natural cluster structures in the rings of regular functions on simple complex Lie groups and Poisson-Lie structures compatible with these cluster structures. According to our main conjecture, each class in the Belavin-Drinfeld classification of Poisson-Lie structures on $\G$ corresponds to a cluster structure in $\O(\G)$. We prove a reduction theorem explaining how different parts of the conjecture are related to each other. The conjecture is established for $SL_n$, $n<5$, and for any $\G$ in the case of the standard Poisson-Lie structure.

Report this publication

Statistics

Seen <100 times