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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-12,
author = {Viktor Losert},
title = {On derivations and crossed homomorphisms},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {199-217},
zbl = {1209.43002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-12}
}
Viktor Losert. On derivations and crossed homomorphisms. Banach Center Publications, Tome 89 (2010) pp. 199-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-12/