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

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

2010-12-29

arxiv.org/abs/1101.0015v2

Mathematics

Quantum Algebra

20 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Cluster structures on simple complex Lie groups and the Belavin-Drinfeld classification does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cluster structures on simple complex Lie groups and the Belavin-Drinfeld classification, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cluster structures on simple complex Lie groups and the Belavin-Drinfeld classification will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-400148