English

Lie quasi-states

Representation Theory 2009-09-01 v2 Symplectic Geometry

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.

Keywords

Cite

@article{arxiv.0906.4901,
  title  = {Lie quasi-states},
  author = {Michael Entov and Leonid Polterovich},
  journal= {arXiv preprint arXiv:0906.4901},
  year   = {2009}
}

Comments

Minor corrections

R2 v1 2026-06-21T13:18:13.436Z