PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (210)
Orphanage
Unclass'd (1)
Unproven (472)
Corrections (38)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Low Entry average rating: No information on entry rating
regular representation (Definition)

Given a group $ G$, the regular representation of $ G$ over a field $ K$ is the representation $ \rho: G \longrightarrow \operatorname{GL}(K^G)$ whose underlying vector space $ K^G$ is the $ K$-vector space of formal linear combinations of elements of $ G$, defined by

$\displaystyle \rho(g)\left(\sum_{i=1}^n k_i g_i\right) := \sum_{i=1}^n k_i (g g_i) $
for $ k_i \in K$, $ g, g_i \in G$.

Equivalently, the regular representation is the induced representation on $ G$ of the trivial representation on the subgroup $ \{1\}$ of $ G$.



"regular representation" is owned by djao.
(view preamble)

View style:

Log in to rate this entry.
(view current ratings)

Cross-references: subgroup, induced representation, linear combinations, vector space, representation, field, group
There are 6 references to this entry.

This is version 2 of regular representation, born on 2002-02-05, modified 2002-02-05.
Object id is 1828, canonical name is RegularRepresentation.
Accessed 3522 times total.

Classification:
AMS MSC: 20C99 (Group theory and generalizations :: Representation theory of groups :: Miscellaneous)
Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)