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, Tome 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.
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, Tome 19 (2009) no. 3, pp. 613-637. http://geodesic.mathdoc.fr/item/JOLT_2009_19_3_a9/
@article{JOLT_2009_19_3_a9,
author = {Michael Entov and Leonid Polterovich},
title = {Lie {Quasi-States}},
journal = {Journal of Lie Theory},
pages = {613--637},
year = {2009},
volume = {19},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2009_19_3_a9/}
}
TY - JOUR
AU - Michael Entov
AU - Leonid Polterovich
TI - Lie Quasi-States
JO - Journal of Lie Theory
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