In this paper we prove that if A is any algebra with involution * satisfying a non-trivial polynomial identity, then its sequence of *-codimensions is eventually non-decreasing. Furthermore, by making use of the *-exponent we reconstruct the only two *-algebras, up to T*-equivalence, generating varieties of almost polynomial growth. As a third result we characterize the varieties of algebras with involution whose exponential growth is bounded by 2.
Giambruno A., La Mattina D. (2020). Codimensions of star-algebras and low exponential growth. ISRAEL JOURNAL OF MATHEMATICS, 239(1), 1-20 [10.1007/s11856-020-2023-y].
Codimensions of star-algebras and low exponential growth
Giambruno A.;La Mattina D.
2020-01-01
Abstract
In this paper we prove that if A is any algebra with involution * satisfying a non-trivial polynomial identity, then its sequence of *-codimensions is eventually non-decreasing. Furthermore, by making use of the *-exponent we reconstruct the only two *-algebras, up to T*-equivalence, generating varieties of almost polynomial growth. As a third result we characterize the varieties of algebras with involution whose exponential growth is bounded by 2.
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