On the lengths of descendingly flexible and descendingly alternative algebras

Alexander Guterman; Svetlana Zhilina

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arXiv · 2312.03170

On the lengths of descendingly flexible and descendingly alternative algebras

Alexander Guterman·Svetlana Zhilina

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Abstract

We introduce the classes of descendingly flexible and descendingly alternative algebras over an arbitrary field $\mathbb{F}$. We suggest a new method based on the sequence of differences between the dimensions of the linear spans of words, which allows us to obtain upper bounds on the lengths of these algebras. We also present an example of an algebra of arbitrarily large dimension such that these bounds are achieved on it asymptotically.

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Alexander Guterman, Svetlana Zhilina. 2023-12-05. On the lengths of descendingly flexible and descendingly alternative algebras. https://arxiv.org/abs/2312.03170

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