Factor representation
From HandWiki
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.
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