On three-dimensional associative algebras

Key Points

The paper presents a comprehensive list of three-dimensional associative algebras with their canonical representatives.
It focuses on fields with characteristics different from two and three, revealing new classifications.
Comparisons are made between the findings and established classifications over complex numbers as well as nilpotent cases.
This research contributes insight into the structure and classification of algebras across various fields.

Abstract

This paper addresses the classification problem of associative algebras over arbitrary base fields. We present a list of three-dimensional associative algebras with canonical representatives of the isomorphism classes for fields of characteristic different from two and three. We also compare our lists with the most recent classifications over the complex numbers and with the nilpotent case over arbitrary base fields in dimension three, adding some comments.

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Cite This Study

Bekbaev et al. (Wed,) studied this question.

synapsesocial.com/papers/68f6196ee0bbbc94fac3628b https://doi.org/https://doi.org/10.48550/arxiv.2508.04104