Multivector Contractions Revisited, Part I

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2024-10-24 DOI:10.1007/s00006-024-01357-4

André L. G. Mandolesi

引用次数: 0

Abstract

We reorganize, simplify and expand the theory of contractions or interior products of multivectors, and related topics like Hodge star duality. Many results are generalized and new ones are given, like: geometric characterizations of blade contractions and regressive products, higher-order graded Leibniz rules, determinant formulas, improved complex star operators, etc. Different contractions found in the literature are discussed and compared, in special those of Clifford Geometric Algebra. Applications of the theory are developed in a follow-up paper.

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重温多向量收缩，第一部分

我们重新组织、简化和扩展了多向量的收缩或内部积理论，以及霍奇星对偶性等相关主题。我们对许多结果进行了归纳，并给出了新的结果，如：叶片收缩和回归积的几何特征、高阶分级莱布尼兹规则、行列式公式、改进的复星算子等。讨论并比较了文献中的不同收缩，特别是克利福德几何代数的收缩。该理论的应用将在后续论文中展开。

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.