几何代数中的扩张子
Extensor in Geometric Algebras
摘要：
本文是八篇系列文章中的第三篇，介绍了光滑流形微分几何公式化所需的扩张子理论的一些基本概念。引入并详细研究了作用于实向量空间V上的线性算子（1，1）-扩张算子的扩张算子和推广算子等关键概念。此外，我们引入了（1，1）-扩张子的行列式的概念和标准和度量霍奇（星）算子的概念，揭示了它们之间的一个非平凡的和有用的关系。
英文摘要：
This paper, the third in a series of eight introduces some of the basic concepts of the theory of extensors needed for our formulation of the differential geometry of smooth manifolds . Key notions such as the extension and generalization operators of a given linear operator (a (1,1)-extensor) acting on a real vector space V are introduced and studied in details. Also, we introduce the notion of the determinant of a (1,1)-extensor and the concepts of standard and metric Hodge (star) operators, disclosing a non trivial and useful relation between them.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
