Rota-Baxter Operators of Nonzero Weight on the Split Octonions

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2025-05-24 DOI:10.1007/s00006-025-01389-4

A. S. Panasenko

引用次数: 0

Abstract

We describe Rota-Baxter operators on split octonions. It turns out that up to some transformations there exists exactly one such non-splitting operator over any field. We also obtain a description of all decompositions of split octonions over a quadratically closed field of characteristic different from 2 into a sum of two subalgebras, which describes the splitting Rota-Baxter operators. It completes the classification of Rota-Baxter operators on composition algebras of any weight.

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分割八元上非零权的Rota-Baxter算子

我们描述分裂八元数上的Rota-Baxter算子。结果表明，对于某些变换，在任何域上都存在一个这样的非分裂算子。我们还得到了特征不等于2的二次闭域上所有分裂八元数分解为两个子代数和的描述，它描述了分裂Rota-Baxter算子。完成了任意权值复合代数上Rota-Baxter算子的分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.