# Factor representation

From Encyclopedia of Mathematics

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.

**How to Cite This Entry:**

Factor representation.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Factor_representation&oldid=14007

This article was adapted from an original article by A. Shtern (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article