Let A be an associative algebra with superinvolution ∗ over a field of characteristic zero and let c_n∗(A) be its sequence of corresponding ∗-codimensions. In case A is finite dimensional, we prove that such sequence is polynomially bounded if and only if the variety generated by A does not contain three explicitly described algebras with superinvolution. As a consequence we find out that no intermediate growth of the ∗-codimensions between polynomial and exponential is allowed.
Giambruno, A., Ioppolo, A., La Mattina, D. (2016). Varieties of Algebras with Superinvolution of Almost Polynomial Growth. ALGEBRAS AND REPRESENTATION THEORY, 19(3), 599-611 [10.1007/s10468-015-9590-3].
Varieties of Algebras with Superinvolution of Almost Polynomial Growth
GIAMBRUNO, Antonino;Ioppolo, Antonio;LA MATTINA, Daniela
2016-01-01
Abstract
Let A be an associative algebra with superinvolution ∗ over a field of characteristic zero and let c_n∗(A) be its sequence of corresponding ∗-codimensions. In case A is finite dimensional, we prove that such sequence is polynomially bounded if and only if the variety generated by A does not contain three explicitly described algebras with superinvolution. As a consequence we find out that no intermediate growth of the ∗-codimensions between polynomial and exponential is allowed.
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