arXiv math-ph/02120432002-12-18math-phmath.MP

欧氏Clifford代数

Euclidean Clifford Algebra

V. V. Fernández, A. M. Moya, W. A. Rodrigues

备注：: Latex accent in author(s) was introduced Latex commands in abstract were corrected
发表信息：: Advances in Applied Clifford Algebras 11(S3),1-21 (2001)

摘要：

设$V$是$n$维实向量空间.本文对$V,$上给定的欧氏结构引入了\emph{euclidean} Clifford代数$\mathcal{C\ell}(V,G_{E})$的概念，即，对$(V,G_{E})$，其中$G_{E}$是$V$的欧几里德度量（也称为欧几里德标量积）。我们的$\mathcal{C\ell}(V,G_{E})$结构被设计成一个强大的计算工具。我们开始介绍的概念，\emph{multivectors}在$V.$这些对象是一个线性空间的元素，在实数域，表示为$\bigwedge V.$。我们还介绍了，外部和欧几里德标量积的多向量的概念。这允许在$\bigwedge V,$上引入两个\emph{contraction operators}和欧几里得\emph{interior}代数的概念。有了这些概念，欧氏Clifford积就很容易被引入。我们用相当多的细节计算出了几个重要的恒等式和有用的公式，以帮助读者发展关于这个问题的技能，为阅读本系列的以下论文做好准备。

英文摘要：

Let $V$ be a $n$-dimensional real vector space. In this paper we introduce the concept of \emph{euclidean} Clifford algebra $\mathcal{C\ell}(V,G_{E})$ for a given euclidean structure on $V,$ i.e., a pair $(V,G_{E})$ where $G_{E}$ is a euclidean metric for $V$ (also called an euclidean scalar product). Our construction of $\mathcal{C\ell}(V,G_{E})$ has been designed to produce a powerful computational tool. We start introducing the concept of \emph{multivectors} over $V.$ These objects are elements of a linear space over the real field, denoted by $\bigwedge V.$ We introduce moreover, the concepts of exterior and euclidean scalar product of multivectors. This permits the introduction of two \emph{contraction operators} on $\bigwedge V,$ and the concept of euclidean \emph{interior} algebras. Equipped with these notions an euclidean Clifford product is easily introduced. We worked out with considerable details several important identities and useful formulas, to help the reader to develope a skill on the subject, preparing himself for the reading of the following papers in this series.

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。

摘要：

英文摘要：

相关论文