%0 Journal Article
%T Antisymmetric elements in group rings with an orientation morphism
%A O. Broche
%A E. Jespers
%A M. Ruiz
%J Mathematics
%D 2007
%I arXiv
%X Let $R$ be a commutative ring, $G$ a group and $RG$ its group ring. Let $\phi_{\sigma} : RG\to RG$ denote the involution defined by $\phi_{\sigma} (\sum r_{g}g) = \sum r_{g} \sigma (g) g^{-1}$, where $\sigma:G\to \{\pm 1\}$ is a group homomorphism (called an orientation morphism). An element $x$ in $RG$ is said to be antisymmetric if $\phi_{\sigma} (x) =-x$. We give a full characterization of the groups $G$ and its orientations for which the antisymmetric elements of $RG$ commute.
%U http://arxiv.org/abs/0705.3106v1