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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
On Central Polynomials And Codimension Growth, Fabrizio Martino
On Central Polynomials And Codimension Growth, Fabrizio Martino
Turkish Journal of Mathematics
Let $A$ be an associative algebra over a field of characteristic zero. A central polynomial is a polynomial of the free associative algebra that takes central values of $A.$ In this survey, we present some recent results about the exponential growth of the central codimension sequence and the proper central codimension sequence in the setting of algebras with involution and algebras graded by a finite group.
Nilpotent Varieties And Metabelian Varieties, Angela Valenti, Sergey Mishchenko
Nilpotent Varieties And Metabelian Varieties, Angela Valenti, Sergey Mishchenko
Turkish Journal of Mathematics
We deal with varieties of nonassociative algebras having polynomial growth of codimensions. We describe some results obtained in recent years in the class of left nilpotent algebras of index two. Recently the authors established a correspondence between the growth rates for left nilpotent algebras of index two and the growth rates for commutative or anticommutative metabelian algebras that allows to transfer the results concerning varieties of left nilpotent algebras of index two to varieties of commutative or anticommutative metabelian algebras.