On derivations and crossed homomorphisms

• Autorzy: Viktor Losert
• Języki publikacji: EN

Abstrakty

EN

We discuss some results about derivations and crossed homomorphisms arising in the context of locally compact groups and their group algebras, in particular, L¹(G), the von Neumann algebra VN(G) and actions of G on related algebras. We answer a question of Dales, Ghahramani, Grønbæk, showing that L¹(G) is always permanently weakly amenable. Then we show that for some classes of groups (e.g. IN-groups) the homology of L¹(G) with coefficients in VN(G) is trivial. But this is no longer true, in general, if VN(G) is replaced by other von Neumann algebras, like ℬ(L²(G)). Finally, as an example of a non-discrete, non-amenable group, we investigate the case of G = SL(2,ℝ) where the situation is rather different.

Kategorie tematyczne

• 46L55: Noncommutative dynamical systems
• 46H99: None of the above, but in this section
• 22F05: General theory of group and pseudogroup actions
• 43A20: L 1 -algebras on groups, semigroups, etc.
• 47B47: Commutators, derivations, elementary operators, etc.
• 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 91
• Numer: 1
• Strony: 199-217

Daty

wydano

2010

Twórcy

autor

Viktor Losert

• Fakultät für Mathematik, Universität Wien, Nordbergstr. 15, A 1090 Wien, Austria

Identyfikatory

DOI

10.4064/bc91-0-12