Talk:Group ring

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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)

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)

There used to be separate group ring and group algebra articles; then they were merged. We need group rings such as Z[G] for abstract algebra. So, I think we should probably go back, now, to separate pages. Charles Matthews 07:47, 10 Sep 2004 (UTC)

My proposal was moving this page to group algebra and keeping only that one article as long as it doesn't get too long. I guess we could turn it into a disambiguation page as well, but I think I'd prefer some common text. For example, all group algebras are commutative if G is abelian (with the converse being true in the non-pathological cases), and for finite groups, all group algebras coincide (if considered over the complex numbers).

Maybe you want to fix the group ring section? Some previous author seems to have focussed on group rings over a field, but in my experience, the most common case is ZG, so maybe at least that case should be explained in a bit more detail. Prumpf 11:14, 10 Sep 2004 (UTC)

A very common case is CG, since this is the fundamental object of study in complex group representations. This probably explains the bias. Ben 11:26, 11 August 2006 (UTC)

The section 'Representations of a group ring' (the one after 'Representations of a group algebra') only talks about representations of group algebras, and doesn't say too much not said earlier. I'm not sure if the sections should merged, or if the second section should be rewritten to talk about modular systems or just integral representations. JackSchmidt 01:58, 8 July 2007 (UTC)

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

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)

Perhaps the page could use a clean-up in terms of consistency with the PNG-style equations (small/large) and in terms of R[G] versus RG? If no-one objects, I'll go ahead and do this. Xantharius 17:18, 4 June 2007 (UTC)

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)

Okay. And on R[G] vs. RG, I concur. :) Xantharius 18:59, 4 June 2007 (UTC)

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)