Abstract In most cases, the Lipschitz monoid Lip(V,Q)documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$textrm{Lip}(V,Q)$$end{document} is the multiplicative monoid (or semi-group) generated in the Clifford algebra Cl(V,Q)documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$textrm{Cl}(V,Q)$$end{document} by the vectors of V. But the elements of Lip(V,Q)documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$textrm{Lip}(V,Q)$$end{document} satisfy many other characteristic properties, very different from one another, which may as well be used as definitions of Lip(V,Q)documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$textrm{Lip}(V,Q)$$end{document}. The present work proposes several characteristic properties, and explores some of the ways that enable us to link one property to another.
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