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

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. 

