This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
This article, although tersely written, is not advanced material. It covers a topic that is commonly taught to second and third year undergraduates, and represents maybe one or two lectures worth of material. This article, as written, should be easy to understand by anyone who has been exposed to introductory group theory. linas 05:14, 26 Jan 2005 (UTC)
Quick question: why can we not define the character group when G is not commutative? What fails? 219.117.195.84 ( talk) 15:18, 7 July 2009 (UTC)
Conjugacy classes: In the preliminaries section, G is introduced as an abelian group, and then it is observed that a character is constant on the conjugacy classes. Since there is only a single element in each conjugacy class of an abelian group, the statement is empty. I don't know the subject, so I can't correct it: I don't know what was intended. Yasmar ( talk) 10:14, 25 February 2012 (UTC)
The comment(s) below were originally left at Talk:Character group/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
Suffers from the identity crisis. Is this about finite groups? Abelian groups? Dirichlet characters? Connections with related notions have to be explained. Arcfrk 07:12, 25 May 2007 (UTC) |
Last edited at 22:44, 28 May 2007 (UTC). Substituted at 01:52, 5 May 2016 (UTC)
There is another definition of characters used in the literature which is slightly different that the one used in this article. These are homomorphisms
which is a subgroup of . Algebraically, they contain the same information for many cases, but having as the target is useful while studying tori. For example, the dual torus of a torus where is a lattice can be found by looking at the character group
One reference is Birkenhake's Complex Abelian Varieties. Kaptain-k-theory ( talk) 20:46, 25 June 2021 (UTC)
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
This article, although tersely written, is not advanced material. It covers a topic that is commonly taught to second and third year undergraduates, and represents maybe one or two lectures worth of material. This article, as written, should be easy to understand by anyone who has been exposed to introductory group theory. linas 05:14, 26 Jan 2005 (UTC)
Quick question: why can we not define the character group when G is not commutative? What fails? 219.117.195.84 ( talk) 15:18, 7 July 2009 (UTC)
Conjugacy classes: In the preliminaries section, G is introduced as an abelian group, and then it is observed that a character is constant on the conjugacy classes. Since there is only a single element in each conjugacy class of an abelian group, the statement is empty. I don't know the subject, so I can't correct it: I don't know what was intended. Yasmar ( talk) 10:14, 25 February 2012 (UTC)
The comment(s) below were originally left at Talk:Character group/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
Suffers from the identity crisis. Is this about finite groups? Abelian groups? Dirichlet characters? Connections with related notions have to be explained. Arcfrk 07:12, 25 May 2007 (UTC) |
Last edited at 22:44, 28 May 2007 (UTC). Substituted at 01:52, 5 May 2016 (UTC)
There is another definition of characters used in the literature which is slightly different that the one used in this article. These are homomorphisms
which is a subgroup of . Algebraically, they contain the same information for many cases, but having as the target is useful while studying tori. For example, the dual torus of a torus where is a lattice can be found by looking at the character group
One reference is Birkenhake's Complex Abelian Varieties. Kaptain-k-theory ( talk) 20:46, 25 June 2021 (UTC)