On derivations and crossed homomorphisms

Viktor Losert. "On derivations and crossed homomorphisms." Banach Center Publications 91.1 (2010): 199-217. <http://eudml.org/doc/282535>.

@article{ViktorLosert2010,
abstract = {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.},
author = {Viktor Losert},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {199-217},
title = {On derivations and crossed homomorphisms},
url = {http://eudml.org/doc/282535},
volume = {91},
year = {2010},
}

TY - JOUR
AU - Viktor Losert
TI - On derivations and crossed homomorphisms
JO - Banach Center Publications
PY - 2010
VL - 91
IS - 1
SP - 199
EP - 217
AB - 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.
LA - eng
UR - http://eudml.org/doc/282535
ER -