Group algebras whose units satisfy a Laurent Polynomial Identity

2017/12/13 by Broche, Osnel, Gonçalves, Jairo Z., del Río, Ángel
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1712.04849

Abstract

Let KG be the group algebra of a torsion group G over a field K. We show that if the units of KG satisfy a Laurent polynomial identity which is not satisfied by the units of the relative free algebra K[α,β: α²=β²=0] then KG satisfies a polynomial identity. This extends Hartley Conjecture which states that if the units of KG satisfies a group identity then KG satisfies a polynomial identity. As an application of our results we prove that if the units of KG satisfies a Laurent polynomial identity with a support of cardinality at most 3 then KG satisfies a polynomial identity.

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