# On derivations and crossed homomorphisms

Banach Center Publications (2010)

- Volume: 91, Issue: 1, page 199-217
- ISSN: 0137-6934

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topViktor 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 -

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