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Difference between revisions of "Non-degenerate representation"

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A [[Linear representation|linear representation]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066990/n0669901.png" /> of a group (ring, algebra, semi-group) <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066990/n0669902.png" /> in a vector space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066990/n0669903.png" /> such that if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066990/n0669904.png" /> for some <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066990/n0669905.png" /> and all <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066990/n0669906.png" />, then <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n066/n066990/n0669907.png" />.
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A [[Linear representation|linear representation]] $\pi$ of a group (ring, algebra, semi-group) $X$ in a vector space $E$ such that if $\pi(x)\xi=0$ for some $\xi\in E$ and all $x\in X$, then $\xi=0$.

Latest revision as of 12:59, 19 April 2014

A linear representation $\pi$ of a group (ring, algebra, semi-group) $X$ in a vector space $E$ such that if $\pi(x)\xi=0$ for some $\xi\in E$ and all $x\in X$, then $\xi=0$.

How to Cite This Entry:
Non-degenerate representation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Non-degenerate_representation&oldid=13800
This article was adapted from an original article by A.I. Shtern (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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