Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 613-637 |
Number of pages | 25 |
Journal | Journal of Lie Theory |
Volume | 19 |
Issue number | 3 |
State | Published - 2009 |
Keywords
- Gleason theorem
- Lie algebra
- Maslov index
- Quasi-state
ASJC Scopus subject areas
- Algebra and Number Theory