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QuasiI-State Rigidity for Finite-Dimensional Lie Algebras

Michael Björklund (Institutionen för matematiska vetenskaper, Analys och sannolikhetsteori) ; T. Hartnick
Israel Journal of Mathematics (0021-2172). Vol. 221 (2017), 1, p. 25-57.
[Artikel, refereegranskad vetenskaplig]

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.

Denna post skapades 2017-10-16.
CPL Pubid: 252546


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