分野別セミナー

Let $G$ be a locally compact group, $L(G)$ be its group von Neumann algebra. In this talk, we consider the following question: When is $L(G)$ a factor? We define a locally compact group G is almost unimodular if the
kernel of modular function $\Delta_G$ is open in $G$. We provide an answer to the above question when $G$ is second countable, almost unimodular and admits a sufficiently large non-unimodular part. Moreover, when $L(G)$ is a factor, we obtain the formula of the S-invariant of $L(G)$.