QuasiI-State Rigidity for Finite-Dimensional Lie Algebras
Journal article, 2017

We say that a Lie algebra g is quasi-state rigid if every Ad-invariant continuous Lie quasi-state on it is the directional derivative of a homogeneous quasimorphism. Extending work of Entov and Polterovich, we show that every reductive Lie algebra, as well as the algebras C-n x u( n), n = 1, are rigid. On the other hand, a Lie algebra which surjects onto the three-dimensional Heisenberg algebra is not rigid. For Lie algebras of dimension <= 3 and for solvable Lie algebras which split over a codimension one abelian ideal, we show that this is the only obstruction to rigidity.

Author

Michael Björklund

Chalmers, Mathematical Sciences, Analysis and Probability Theory

University of Gothenburg

T. Hartnick

Technion – Israel Institute of Technology

Israel Journal of Mathematics

0021-2172 (ISSN) 15658511 (eISSN)

Vol. 221 1 25-57

Subject Categories

Mathematics

DOI

10.1007/s11856-017-1542-7

More information

Latest update

5/9/2018 6