Polynomial growth and star-varieties

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• 作者：Daniela La Mattina^a ; ¹ ; ^{daniela.lamattina@unipa.it" class="auth_mail" title="E-mail the corresponding author} ; Fabrizio Martino^b ; ² ; ^{fabmartino@ime.unicamp.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Primary ; 16R10 ; 16R50 ; secondary ; 16W10
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：220
• 期：1
• 页码：246-262
• 全文大小：435 K

文摘

Let V$\mathcal{V}$ be a variety of associative algebras with involution over a field F   of characteristic zero and let $c_n^{鈦?/mo>}(\mathcal{V})$, n=1,2,…$n=1,2,\dots$, be its 鈦?codimension sequence. Such a sequence is polynomially bounded if and only if V$\mathcal{V}$ does not contain the commutative algebra F⊕F$F\oplus F$, endowed with the exchange involution, and M  , a suitable 4-dimensional subalgebra of the algebra of 4×4$4\times 4$ upper triangular matrices. Such algebras generate the only varieties of 鈦?algebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety is polynomially bounded. In this paper we completely classify all subvarieties of the 鈦?varieties of almost polynomial growth by giving a complete list of finite dimensional 鈦?algebras generating them.