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Difference between revisions of "Linear representation"

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====References====
 
====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  C.W. Curtis,  I. Reiner,  "Methods of representation theory" , '''1–2''' , Wiley (Interscience)  (1981–1987)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  J.-P. Serre,  "Répresentations linéaires des groupes finis" , Hermann  (1967)</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  A.I. Shtern,  "Theory of group representations" , Springer  (1982)  (Translated from Russian)</TD></TR></table>
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  C.W. Curtis,  I. Reiner,  "Methods of representation theory" , '''1–2''' , Wiley (Interscience)  (1981–1987)</TD></TR>
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<TR><TD valign="top">[a2]</TD> <TD valign="top">  J.-P. Serre,  "Répresentations linéaires des groupes finis" , Hermann  (1967)</TD></TR>
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<TR><TD valign="top">[a3]</TD> <TD valign="top">  A.I. Shtern,  "Theory of group representations" , Springer  (1982)  (Translated from Russian)</TD></TR>
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</table>
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[[Category:Group theory and generalizations]]

Latest revision as of 19:18, 25 October 2014

A homomorphism $\pi$ of a group (respectively an algebra, ring, semi-group) $X$ into the group of all invertible linear operators on a vector space $E$ (respectively, into the algebra, ring, multiplicative semi-group of all linear operators on $E$). If $E$ is a topological vector space, then a linear representation of $X$ on $E$ is a representation whose image contains only continuous linear operators on $E$. The space $E$ is called the representation space of $\pi$ and the operators $\pi(x)$, $x\in X$, are called the operators of the representation $\pi$.

References

[1] A.A. Kirillov, "Elements of the theory of representations" , Springer (1976) (Translated from Russian)


Comments

References

[a1] C.W. Curtis, I. Reiner, "Methods of representation theory" , 1–2 , Wiley (Interscience) (1981–1987)
[a2] J.-P. Serre, "Répresentations linéaires des groupes finis" , Hermann (1967)
[a3] A.I. Shtern, "Theory of group representations" , Springer (1982) (Translated from Russian)
How to Cite This Entry:
Linear representation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linear_representation&oldid=32577
This article was adapted from an original article by A.I. Shtern (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article