Difference between revisions of "Factor representation"
From Encyclopedia of Mathematics
(Importing text file) |
Ulf Rehmann (talk | contribs) m (tex encoded by computer) |
||
| Line 1: | Line 1: | ||
| − | A | + | <!-- |
| + | f0380701.png | ||
| + | $#A+1 = 12 n = 0 | ||
| + | $#C+1 = 12 : ~/encyclopedia/old_files/data/F038/F.0308070 Factor representation | ||
| + | Automatically converted into TeX, above some diagnostics. | ||
| + | Please remove this comment and the {{TEX|auto}} line below, | ||
| + | if TeX found to be correct. | ||
| + | --> | ||
| + | |||
| + | {{TEX|auto}} | ||
| + | {{TEX|done}} | ||
| + | |||
| + | 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