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Lie quasi-states. (English) Zbl 1182.53075
Summary: 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.

MSC:
53D12 Lagrangian submanifolds; Maslov index
17B99 Lie algebras and Lie superalgebras
15A27 Commutativity of matrices
15B99 Special matrices
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