Glossary of representation theory

This is a glossary of <a href="/facts/Representation_theory/3ydLtaGH">representation theory</a> in <a href="/facts/Mathematics/pxTouaz4">mathematics</a>.
The term "module" is often used synonymously for a representation; for the module-theoretic terminology, see also <a href="/facts/Glossary_of_module_theory/bFmuTYSa">glossary of module theory</a>.
See also <a href="/facts/Glossary_of_Lie_groups_and_Lie_algebras/6xUaAGAC">Glossary of Lie groups and Lie algebras</a>, <a href="/facts/List_of_representation_theory_topics/ypDapK9l">list of representation theory topics</a> and Category:Representation theory.
Notations: We write 
 
 
 
 
 
 G
 
 
 m
 
 
 =
 G
 
 L
 
 1
 
 
 
 
 {\displaystyle \mathbb {G} _{m}=GL_{1}}
 
. Thus, for example, a one-representation (i.e., a character) of a group G is of the form 
 
 
 
 χ
 :
 G
 →
 
 
 G
 
 
 m
 
 
 
 
 {\displaystyle \chi :G\to \mathbb {G} _{m}}
 
.

Glossary of representation theory open-in-new

Glossary of representation theory