标题： Z_2-分级的 Clifford 代数和多重向量结构 显示英文标题

标题： Z_2-gradings of Clifford algebras and multivector structures

摘要： 设 Cl(V,g) 是赋以非退化度量 g 的实向量空间 V 所对应的实 Clifford 代数。本文研究了 Cl(V,g) 的一类与 V 上的 Grassmann 代数多重向量结构某种程度上相容的 Z_2-分级。通过分类由此产生的所有偶子代数，得到了这类 Z_2-分级的一个完整刻画。还获得了表达此类子代数与 Cl(V,g) 的通常偶部分之间关系的公式。最后，我们利用这一框架定义旋量空间，并通过该代数的 Z_2-分级来参数化 Cl(V,g) 的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.