标题： Z_2-分次的克利福德代数和多矢量结构 显示英文标题

标题： Z_2-gradings of Clifford algebras and multivector structures

摘要： 设 Cl(V,g) 为与实向量空间 V 及其非退化度量 g 关联的实Clifford代数。在本文中，我们研究了 Cl(V,g) 的某种与 V 上Grassmann代数的多向量结构相容的 Z_2-分次。通过分类由此产生的所有偶子代数，得到了此类 Z_2-分次的完整特征。还得到了这些子代数与 Cl(V,g) 的通常偶部分之间的关系表达式。最后，我们利用这个框架来定义旋量空间，并通过该代数的 Z_2-分次来参数化 Cl(V,g) 上所有可能的符号变化。 显示英文摘要

摘要： Let Cl(V,g) be the real Clifford algebra associated to the real vector space V, endowed with a nondegenerate metric g. In this paper, we study the class of Z_2-gradings of Cl(V,g) which are somehow compatible with the multivector structure of the Grassmann algebra over V. A complete characterization for such Z_2-gradings is obtained by classifying all the even subalgebras coming from them. An expression relating such subalgebras to the usual even part of Cl(V,g) is also obtained. Finally, we employ this framework to define spinor spaces, and to parametrize all the possible signature changes on Cl(V,g) by Z_2-gradings of this algebra.