Codimensions of algebras with additional structures

Authors: DANIELA LA MATTINA

Abstract: Let $A$ be an associative algebra endowed with an automorphism or an antiautomorphism $\varphi$ of order $\leq 2.$ One associates to $A,$ in a natural way, a numerical sequence $c^\varphi_n(A),$ $n=1, 2, \ldots$, called the sequence of $\varphi$-codimensions of $A$ which is the main tool for the quantitative investigation of the polynomial identities satisfied by $A$. In \cite{GLM} it was proved that such a sequence is eventually nondecreasing in case $\varphi$ is an antiautomorphism. Here we prove that it still holds in case $\varphi$ is an automorphism and present some recent results about the asymptotics of $c^\varphi_n(A)$.

Keywords: Polynomial identity, $\varphi$-identity, growth

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