Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Antisymmetric elements in group rings with an orientation morphism   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.

36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat