Journal of Lie Theory

no. 3
Lie Quasi-States
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 
@article{JOLT_2009_19_3_a9,
     author = {M. Entov and L. Polterovich},
     title = {Lie {Quasi-States}},
     journal = {Journal of Lie Theory},
     pages = {613--637},
     year = {2009},
     volume = {19},
     number = {3},
     doi = {10.5802/jolt.571},
     zbl = {1182.53075},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.571/}
}
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M. Entov; L. 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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