Difference between revisions of "Factor representation"
From Encyclopedia of Mathematics
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+ | A [[Linear representation|linear representation]] \pi | ||
+ | of a group or an algebra X | ||
+ | on a Hilbert space H | ||
+ | such that the [[Von Neumann algebra|von Neumann algebra]] on H | ||
+ | generated by the family \pi ( X) | ||
+ | is a [[Factor|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. |
Latest revision as of 19:38, 5 June 2020
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
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