Let V be a variety of associative algebras with involution over a field F of characteristic zero and let c_n*(V), n= 1, 2, . ., be its *-codimension sequence. Such a sequence is polynomially bounded if and only if V does not contain the commutative algebra F⊕ F, endowed with the exchange involution, and M, a suitable 4-dimensional subalgebra of the algebra of 4 ×4 upper triangular matrices. Such algebras generate the only varieties of *-algebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety is polynomially bounded. In this paper we completely classify all subvarieties of the *-varieties of almost polynomial growth by giving a complete list of finite dimensional *-algebras generating them.
La Mattina, D., Martino, F. (2016). Polynomial growth and star-varieties. JOURNAL OF PURE AND APPLIED ALGEBRA, 220(1), 246-262 [10.1016/j.jpaa.2015.06.008].
Polynomial growth and star-varieties
LA MATTINA, Daniela;MARTINO, Fabrizio
2016-01-01
Abstract
Let V be a variety of associative algebras with involution over a field F of characteristic zero and let c_n*(V), n= 1, 2, . ., be its *-codimension sequence. Such a sequence is polynomially bounded if and only if V does not contain the commutative algebra F⊕ F, endowed with the exchange involution, and M, a suitable 4-dimensional subalgebra of the algebra of 4 ×4 upper triangular matrices. Such algebras generate the only varieties of *-algebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety is polynomially bounded. In this paper we completely classify all subvarieties of the *-varieties of almost polynomial growth by giving a complete list of finite dimensional *-algebras generating them.File | Dimensione | Formato | |
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