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Quotient representation

From Encyclopedia of Mathematics
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A quotient representation of a representation of a group (cf. Representation of a group), or algebra, is a representation of defined as follows. Let be the (topological) vector space of the representation ; then is a representation in a (topological) vector space that is the quotient space of by some invariant subspace of (cf. Invariant subspace of a representation), defined by the formula for all , . If is a continuous representation, then so is any quotient representation of it.

How to Cite This Entry:
Quotient representation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quotient_representation&oldid=32502
This article was adapted from an original article by A.I. Shtern (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article