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| Paper IPM / M / 17640 | ||||||||||||||||||
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Let F be an infinite field of characteristic p≠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 U(FG) and on symmetric units U+(FG)={α∈U(FG)∣α∗=α} have been considered. Here, we investigate normalized Laurent polynomial identities (as a generalization of group identities) on U+(FG) under the conditions that either p>2 or F is algebraically closed. For instance, we show that if G is torsion and U+(FG) satisfies a normalized Laurent polynomial identity, then U+(FG) satisfies a group identity and FG satisfies a polynomial identity.
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