
Journal of Lie Theory 19 (2009), No. 3, 613637 Copyright Heldermann Verlag 2009 Lie QuasiStates Michael Entov Dept. of Mathematics, Technion  Israel Inst. of Technology, Haifa 32000, Israel entov@math.technion.ac.il Leonid Polterovich School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel and: Dept. of Mathematics, University of Chicago, Chicago, IL 60637, U.S.A. polterov@runbox.com Lie quasistates on a real Lie algebra are functionals which are linear on any abelian subalgebra. We show that on the symplectic Lie algebra of rank at least 3 there is only one continuous nonlinear Lie quasistate (up to a scalar factor, modulo linear functionals). It is related to the asymptotic Maslov index of paths of symplectic matrices. Keywords: Quasistate, Lie algebra, Maslov index, Gleason theorem. MSC: 53D12, 17B99, 15A27, 15B99 [ Fulltextpdf (257 KB)] for subscribers only. 