Star-polynomial identities: Computing the exponential growth of the codimensions

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• 作者：A. Giambruno^a ; ^{antonio.giambruno@unipa.it" class="auth_mail" title="E-mail the corresponding author} ; C. Polcino Milies^b ; ^c ; ^{polcino@ime.usp.br" class="auth_mail" title="E-mail the corresponding author} ; ^{polcino@ufabc.edu.br" class="auth_mail" title="E-mail the corresponding author} ; A. Valenti^d ; ^{angela.valenti@unipa.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 16R10 ; 16R50 ; secondary ; 16P90
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：469
• 期：Complete
• 页码：302-322
• 全文大小：443 K

文摘

Can one compute the exponential rate of growth of the ⁎-codimensions of a PI-algebra with involution ⁎ over a field of characteristic zero? It was shown in br0020">[2] that any such algebra A has the same ⁎-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution B  . Here, by exploiting this result we are able to provide an exact estimate of the exponential rate of growth exp^⁎(A)$ex{p}^{⁎}(A)$ of any PI-algebra A   with involution. It turns out that exp^⁎(A)$ex{p}^{⁎}(A)$ is an integer and, in case the base field is algebraically closed, it coincides with the dimension of an admissible subalgebra of maximal dimension of B.