Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3245
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
First Page
1975
Last Page
1984
Recommended Citation
MATTINA, DANIELA LA
(2022)
"Codimensions of algebras with additional structures,"
Turkish Journal of Mathematics: Vol. 46:
No.
5, Article 24.
https://doi.org/10.55730/1300-0098.3245
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss5/24
