We study the ∗-varieties of associative algebras with involution over a field of characteristic zero which are generated by a finite-dimensional algebra. In this setting we give a list of algebras classifying all such ∗-varieties whose sequence of ∗-codimensions is linearly bounded. Moreover, we exhibit a finite list of algebras to be excluded from the ∗-varieties with such property. As a consequence, we find all possible linearly bounded ∗-codimension sequences.
DLAMATTINA, MISSO P (2006). Algebras with involution with linear codimension growth. JOURNAL OF ALGEBRA, 305(305), 270-291 [10.1016/j.jalgebra.2006.06.044].
Algebras with involution with linear codimension growth
LA MATTINA, Daniela;MISSO, Paola
2006-01-01
Abstract
We study the ∗-varieties of associative algebras with involution over a field of characteristic zero which are generated by a finite-dimensional algebra. In this setting we give a list of algebras classifying all such ∗-varieties whose sequence of ∗-codimensions is linearly bounded. Moreover, we exhibit a finite list of algebras to be excluded from the ∗-varieties with such property. As a consequence, we find all possible linearly bounded ∗-codimension sequences.
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