Linear representation
From Encyclopedia of Mathematics
A homomorphism 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=34025
Linear representation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linear_representation&oldid=34025
This article was adapted from an original article by A.I. Shtern (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article