An algebra graded by a group G and endowed with a graded involution * is called a (G, *)-algebra. Here we consider G a finite abelian group and classify the subvarieties of the varieties of almost polynomial growth generated by finite-dimensional (G, *)-algebras. Also, we present, up to equivalence, the complete list of (G, *)-algebras generating varieties of at most linear growth. Along the way, we give a new characterization of varieties of polynomial growth generated by finite-dimensional (G, *)-algebras by considering the structure of the generating algebra.

中文翻译：

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群梯度对合代数余维序列的多项式增长

由群G分级并赋予分级对合 * 的代数称为 ( G , *)-代数。这里我们将G视为有限阿贝尔群，并对由有限维 ( G , *)-代数生成的几乎多项式增长的簇的子簇进行分类。此外，我们还提出了直到等价性为止，生成最多线性增长簇的( G , *)-代数的完整列表。在此过程中，我们通过考虑生成代数的结构，给出了由有限维 ( G , *) 代数生成的多项式增长变体的新表征。