Abstract
We study polynomial identities of algebras with involution of nonassociative algebras over a field of characteristic zero. We prove that the growth of the sequence of ⁎-codimensions of a finite-dimensional algebra is exponentially bounded. We construct a series of finite-dimensional algebras with fractional ⁎-PI-exponent. We also construct a family of infinite-dimensional algebras Cα such that exp⁎(Cα) does not exist.
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