Department of Mathematics

Algebra

  •  Exotic cluster algebras
  •  12/07/2016
  •  3:00 PM - 3:50 PM
  •  C304 Wells Hall
  •  Idan Eisner, Technion, Haifa, Israel

Using the notion of compatibility between Poisson brackets and cluster algebras in the coordinate rings of simple complex Lie groups, Gekhtman Shapiro and Vainshtein conjectured a correspondence between the two. Poisson Lie groups are classified by the Belavin-Drinfeld classification of solutions to the classical Yang Baxter equation. For a simple complex Lie group G and a Belavin-Drinfeld class, one can define a corresponding Poisson bracket on the ring of regular functions on G. For some of these classes a compatible cluster structure can be constructed. We will describe some of these for G=SLn. In some cases, the compatible structure is a generalized cluster algebra, where the exchange relations are polynomial rather than binomial. We will show this for G=SP6.

 

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