In the last years, the sequence of codimensions of PI-algebras has been studied by several authors and the classification of unitary algebras, up to equivalence, with at most cubic codimension growth was given by Giambruno, La Mattina and Petrogradsky in 2007. In this paper, we establish a new approach by studying the possibilities of specific proper codimensions of a unitary algebra with growth n4 in order to present a complete list of varieties generated by unitary algebras with polynomial growth n4. Also, we classify, up to PI-equivalence, the unitary algebras with growth n5 whose leading coefficient of the polynomial describing the codimension sequence achieves the largest and the smallest possible value.

中文翻译：

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余维数增长较小的酉代数种类

在过去的几年里，几位作者研究了 PI 代数的余维数序列，Giambruno、La Mattina 和 Petrogradsky 在 2007 年给出了直到等价的酉代数的分类，最多具有三次余维数增长。在论文中，我们通过研究具有增长的酉代数的特定适当余量的可能性来建立一种新方法n4为了提供由多项式增长的酉代数生成的完整列表n4. 此外，我们对具有增长的酉代数进行分类，直到 PI 等价n5其描述余维序列的多项式的前导系数达到最大和最小的可能值。