Algebraic automorphisms and $PI$-algebras

This paper is concerned with associative algebras over a field of characteristic zero which possess a $d$-regular algebraic automorphism. (An automorphism is called $d$-regular if the subalgebra of fixed elements satisfies an identity of degree $d$.) It is shown that if an algebra admits a $d$-regular algebraic automorphism such that no root of unity is a multiple root of its minimum polynomial, then it is a $PI$-algebra.
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