Lie quasi-states

Michael Entov, Leonid Polterovich

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 languageEnglish
Pages (from-to)613-637
Number of pages25
JournalJournal of Lie Theory
Issue number3
StatePublished - 2009


  • Gleason theorem
  • Lie algebra
  • Maslov index
  • Quasi-state

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Lie quasi-states'. Together they form a unique fingerprint.

Cite this