Talk:Group ring

message: Some of the edits I just made were based on memory and could thus be slightly wrong.  In particular, I'm not sure about the norm used to define the non-reduced C* algebra.  Prumpf 00:48, 10 Sep 2004 (UTC)
replies: text: It looks right to me. Also various relations between representations weakly contained in the left regular rep and the reduced C*-algebra should be put in at some point.  I also think the name group algebra is preferable to group ring.CSTAR 01:02, 10 Sep 2004 (UTC)
thread_title:  Non-reduced C* algebra norms 

message: Group ring definition does not imply usually that the ring is commutative. Jean-Louis Margot 12:12, 30 Sep 2005 (UTC)
thread_title:  Commutative coefficient ring 

message: This could use a clean up - at the moment it's a bit of a hodge podge of facts and statements. Leland McInnes 21:16, 28 January 2006 (UTC)
replies: text: Sounds like a plan. Go for it. And while I can get in a preference: I think R[G] is nicer. ;-) Leland McInnes 18:37, 4 June 2007 (UTC)
replies: text: Okay. And on R[G] vs. RG, I concur. :) Xantharius 18:59, 4 June 2007 (UTC)
thread_title:  Request for clenaup 

message: In section 'group rings over an infinite group' one may take into account that the statement that C[G] is free of non-trivial idempotents if G is torsion-free is proved for all groups which satisfy the Baum-Connes conjecture. In fact, in that case even the reduced C*-algebra of G is free of nontrivial idempotents. The class of groups which are known to satisfy Baum-Connes is much larger than that of abelian, free, or elementary amenable groups, for instance, it includes amenable groups.  —Preceding unsigned comment added by 134.76.82.127 (talk) 15:19, 17 September 2007 (UTC)
replies: text: That last comment is wrong, Gardam found a counterexample (in positive characteristic) to the unit conjecture, which is stronger than the zero-divisor conjecture. The group in which Gardam found a nontrivial unit is knwon to satisfy the zero-divisor conjecture. jraimbau (talk) 10:47, 16 October 2021 (UTC)
thread_title:  Zero divisor problem 

message: I worked over the definition, added a couple of canonical properties, and removed the "confusing" tag. Hope it's okay. LDH (talk) 02:00, 20 November 2008 (UTC)
thread_title: Tidier now?

message: What if the ring doesn't have any units?=r peterson216.86.177.36 (talk) 22:32, 24 February 2012 (UTC)
thread_title: "Categorically, the group ring construction is left adjoint to "group of units""

message: The article says group rings satisfy ``a universal property, citing Polcino & Sehgal (2002), p. 131. Can somebody with a copy of this text (or somebody who otherwise knows) fill in what the property is?71.36.206.9 (talk) 16:00, 23 August 2012 (UTC)
replies: text: You can have a look in Google Books: http://books.google.com/books?id=7m9P9hM4pCQC&pg=PA131 --Kompik (talk) 06:38, 15 December 2012 (UTC)
thread_title:  Universal property 

message: The "Hopf algebra" material in this article is inconsistent with the article group Hopf algebra, which says that the notions of "group algebra" and "group Hopf algebra" coincide only when the order of the group is finite. Thoughts? Thatsme314 (talk) 05:42, 9 October 2023 (UTC)
replies: text: I think it's best to remove the second part of this sentence in the lede (to wit : "A group algebra over a field has a further structure of a Hopf algebra; in this case, it is thus called a group Hopf algebra." <- "A group algebra over a field has a further structure of a Hopf algebra." The article on "group hopf algebra" doesn't have much additional content compared to that on Hopf algebras. jraimbau (talk) 06:46, 9 October 2023 (UTC)
thread_title:  Hopf algebra