Lecture: Group valued moment maps for even and odd simple G-modules

We are pleased to extend to you an invitation to an enlightening lecture titled "Group valued moment maps for even and odd simple G-modules"

When: 2 March 2026 from 14:00
Where: room S48
Who: Andrey Krutov (Mathematical Institute of Charles University)

Abstract: Let $G$ be a complex simple Lie group, and~$\mathfrak{g}$ its Lie algebra. It is well known that a finite-dimensional $G$-module $V$ carrying anondegenerate invariant bilinear form gives rise to  a Hamiltonian Poisson space with a quadratic moment map $\mu$.We show that under condition $\mathrm{Hom}_\fg(\wedge^3 V, S^3V)=0$ this space can be viewed as a quasi-Poisson space with the same bivector, and with the group valued moment map $\Phi = \exp \circ \mu$. Furthermore, we show that by modifying the bivector by the standard $r$-matrix for $\mathfrak{g}$ one obtains a space with a Poisson action of the Poisson-Lie group $G$,and with the moment map in the sense of Lu taking values in the dual Poisson-Lie group~$G^\ast$. The talk is based on the joint work arXiv:2507.19434 with A. Alekseev (Geneva).