Linear representation
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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
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