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Paper   IPM / M / 17640
School of Mathematics
  Title:   Laurent polynomial identities on symmetric units of group algebras
  Author(s):  Mojtaba Ramezan-Nassab (Joint with M. Akbari-Sehat)
  Status:   To Appear
  Journal: Comm. Algebra
  Supported by:  IPM
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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