I am looking at a von Neumann algebra constructed from a discrete group and a 2cocylce. Does someone know some good references (article, book)? It would be very helpful for me. To be more precise, consider a countable group $G$ and a 2cocycle $\phi :G^2\rightarrow S^1$ where $S^1$ is the group of complex number of modulus 1. You get a representation $\pi$ of the group $G$ in the Hilbert space $l^2(G)$ defined as follow: $$\pi(g)(e_t)=\phi(g,t).e_{gt}$$, where $e_t$ is the canonical hilbert basis of $l^2(G)$. I consider $L_\phi(G)$, the von Neumann algebra generated by $\pi(G)$. I am looking for reference on those kinds of algebra. Thanks, Arnaud
Take the 2minute tour
×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

You can consult the article Bédos, Erik On Følner nets, Szegő's theorem and other eigenvalue distribution theorems. Exposition. Math. 15 (1997), no. 3, 193228. and this recent article: http://arxiv.org/PS_cache/math/pdf/0605/0605145v2.pdf Finally, I believe that the construction is first appeared in ZellerMeier, G. Produits croisés d’une C*algèbre par un groupe d’automorphismes. (French) J. Math. Pures Appl. (9) 47 1968 101–239 


You might find these articles helpful (although it deals with the more general case): Sutherland, Colin E. Cohomology and extensions of von Neumann algebras. I, II. Publ. Res. Inst. Math. Sci. 16 (1980), no. 1, 105133, 135174. 

