Polynomial identities and codimension growth of nonassociative algebras over a field of characteristic zero are considered. A new approach is proposed for constructing nonassociative algebras starting from a given infinite binary word. The sequence of codimensions of such an algebra is closely connected with the combinatorial complexity of the defining word. These constructions give new examples of algebras with abnormal codimension growth. The first important achievement of the given approach is that the algebras under study are finitely generated. The second one is that the asymptotic behavior of codimension sequences is widely different from all previous examples.

中文翻译：

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二进制词的代数和组合性质的恒等式

考虑了特征零域上非关联代数的多项式恒等式和余维增长。提出了一种从给定的无限二进制字开始构造非关联代数的新方法。这种代数的余维序列与定义词的组合复杂性密切相关。这些构造给出了具有异常余维增长的代数的新例子。给定方法的第一个重要成就是所研究的代数是有限生成的。第二个是余维序列的渐近行为与之前所有的例子有很大的不同。