# Difference between revisions of "Factor representation"

A linear representation $\pi$ of a group or an algebra $X$ on a Hilbert space $H$ such that the von Neumann algebra on $H$ generated by the family $\pi ( X)$ is a factor. If this factor is of type $\textrm{ I }$( respectively, $\textrm{ II }$, $\textrm{ III }$, $\textrm{ II } _ {1}$, $\textrm{ II } _ \infty$ etc.), then $\pi$ is called a factor representation of type $\textrm{ I }$, etc.