Quasi-state rigidity for finite-dimensional Lie algebras |
| |
Authors: | Michael Björklund Tobias Hartnick |
| |
Institution: | 1.Department of Mathematical Sciences,Chalmers University of Technology,Gothenburg,Sweden;2.Mathematics Department,Technion—Israel Institute of Technology,Haifa,Israel |
| |
Abstract: | 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 ? 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|