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| Paper IPM / M / 17640 |
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| Abstract: | |
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Let $F$ be an infinite field of characteristic $p \neq 2$, $G$ be a group, and $*$ be an involution of $G$ extended linearly to an involution of the group algebra $FG$. In the literature, group identities on units $\mathcal{U}(FG)$ and on symmetric units $\mathcal{U}^+(FG) = \{\alpha \in \mathcal{U}(FG) \mid \alpha^* = \alpha\}$ have been considered. Here, we investigate normalized Laurent polynomial identities (as a generalization of group identities) on $\mathcal{U}^+(FG)$ under the conditions that either $p > 2$ or $F$ is algebraically closed. For instance, we show that if $G$ is torsion and $\mathcal{U}^+(FG)$ satisfies a normalized Laurent polynomial identity, then $\mathcal{U}^+(FG)$ satisfies a group identity and $FG$ satisfies a polynomial identity.
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