In most cases, the Lipschitz monoid \(\textrm{Lip}(V,Q)\) is the multiplicative monoid (or semi-group) generated in the Clifford algebra \(\textrm{Cl}(V,Q)\) by the vectors of V. But the elements of \(\textrm{Lip}(V,Q)\) satisfy many other characteristic properties, very different from one another, which may as well be used as definitions of \(\textrm{Lip}(V,Q)\). The present work proposes several characteristic properties, and explores some of the ways that enable us to link one property to another.

中文翻译：

---

Clifford 代数中 Lipschitzian 元素的各种特征性质

在大多数情况下，Lipschitz 幺半群\(\textrm{Lip}(V,Q)\)是在 Clifford 代数\(\textrm{Cl}(V,Q)\)中生成的乘法幺半群（或半群）由V的向量。但是\(\textrm{Lip}(V,Q)\)的元素满足许多其他彼此非常不同的特征属性，这些属性也可以用作\(\textrm{Lip}(V,Q)的定义)\)。目前的工作提出了几个特征，并探索了一些使我们能够将一种属性与另一种属性联系起来的方法。