Quotient representation
From Encyclopedia of Mathematics
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=13844
Quotient representation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quotient_representation&oldid=13844
This article was adapted from an original article by A.I. Shtern (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article