Timeline for Bijection between irreducible representations and conjugacy classes of finite groups

7 events

when toggle format	what		by	license	comment
Jul 23, 2012 at 13:00	history	edited	Steven Landsburg	CC BY-SA 3.0	added 83 characters in body
Jul 23, 2012 at 10:08	comment	added	David E Speyer		May I suggest that you then change "matrix rings over division rings" to "matrix rings over $k$"? Since an algebraically closed field has nonnontrivial finite division ring extensions.
Jul 22, 2012 at 23:30	history	edited	Steven Landsburg	CC BY-SA 3.0	added 22 characters in body
Jul 22, 2012 at 23:30	comment	added	Steven Landsburg		David Speyer: Point taken; I've inserted the words "algebraically closed" where I ought to have inserted them in the first place.
Jul 22, 2012 at 22:47	comment	added	David E Speyer		This only works when $k$ is algebraically closed, and the result itself also only works in that generality. For example, over $\mathbb{R}$, the cyclic group of order $3$ has two irreducible representations but still has three conjugacy classes. The error in the argument is that, for a division ring $\Delta$ occuring in the decomposition of $k[G]$, the contribution of $M_n(\Delta)$ to $Z(k[G])$ is $Z(\Delta)$, which may be larger than $k$.
Jul 22, 2012 at 20:50	history	edited	Steven Landsburg	CC BY-SA 3.0	deleted redundant "and another"
Jul 22, 2012 at 17:34	history	answered	Steven Landsburg	CC BY-SA 3.0