Journal of Lie Theory

no. 3
Lie Quasi-States
Michael Entov1; Leonid Polterovich2, 3
1Dept. of Mathematics, Technion -- Israel Inst. of Technology, Haifa 32000, Israel
2School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
3Dept. of Mathematics, University of Chicago, Chicago, IL 60637, U.S.A.
Journal of Lie Theory, Volume 19 (2009) no. 3, pp. 613-637
Lie quasi-states 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 non-linear Lie quasi-state (up to a scalar factor, modulo linear functionals). It is related to the asymptotic Maslov index of paths of symplectic matrices.
DOI: 10.5802/jolt.571
Classification: 53D12, 17B99, 15A27, 15B99
Keywords: Quasi-state, Lie algebra, Maslov index, Gleason theorem

Michael Entov  1 ; Leonid Polterovich  2 , 3

1 Dept. of Mathematics, Technion -- Israel Inst. of Technology, Haifa 32000, Israel
2 School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
3 Dept. of Mathematics, University of Chicago, Chicago, IL 60637, U.S.A. 
Michael Entov; Leonid Polterovich. Lie Quasi-States. Journal of Lie Theory, Volume 19 (2009) no. 3, pp. 613-637. doi: 10.5802/jolt.571
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     year = {2009},
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