Colloquium: Tuesday Nov. 4, 2025 (14:00, room 614). Speaker: Alek Vainshtein (Haifa). Title: “Poisson-Lie groups and cluster structures”.
It is well known that cluster structures and Poisson structures in the algebra of regular functions on a quasi-affine variety are closely related. In this talk, I will discuss this connection for Poisson structures defined on a simple simply connected complex Lie group G by a pair of classical R-matrices. The key element of the construction is a rational Poisson map from the group with a bracket defined by a pair of suitably chosen standard R-matrices to the same group with an arbitrary pair of R-matrices. In the case of G=SL_n one can build explicitly the corresponding cluster structure and prove its regularity and completeness.
Based on joint work with Misha Gekhtman (Notre Dame) and Michael Shapiro (Michigan State University)
