Antisymmetric elements in group rings with an orientation morphism

Details Antisymmetric elements in group rings with an orientation morphism Antisymmetric elements in group rings with an orientation morphism

2007-05-22

arxiv.org/abs/0705.3106v1

Mathematics

K-Theory and Homology

Scientific paper

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.

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