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arXiv · 0705.3106

Antisymmetric elements in group rings with an orientation morphism

O. Broche·E. Jespers·M. Ruiz
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Abstract

Let $R$ be a commutative ring, $G$ a group and $RG$ its group ring. Let $ϕ_σ : RG\to RG$ denote the involution defined by $ϕ_σ (\sum r_{g}g) = \sum r_{g} σ(g) g^{-1}$, where $σ:G\to \{\pm 1\}$ is a group homomorphism (called an orientation morphism). An element $x$ in $RG$ is said to be antisymmetric if $ϕ_σ (x) =-x$. We give a full characterization of the groups $G$ and its orientations for which the antisymmetric elements of $RG$ commute.

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O. Broche, E. Jespers, M. Ruiz. 2007-05-22. Antisymmetric elements in group rings with an orientation morphism. https://arxiv.org/abs/0705.3106

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