Minimal Algorithms for Lipschitz Monoids and Vahlen Monoids

Jacques Helmstetter


Every Clifford algebra $\Cl(V,q)$ contains a Lipschitz monoid $\Lip(V,q)$, which is in general (but not always) the multiplicative monoid generated by all vectors; its even and odd components are closed irreducible algebraic submanifolds. In this article, an algorithm allows to decide whether a given even or odd element of $\Cl(V,q)$ belongs to $\Lip(V,q)$; it is minimal because the number of required verifications is equal to the codimension of the even and odd components of $\Lip(V,q)$. There is an immediate application to Vahlen matrices, since the Vahlen monoid is the image of a Lipschitz monoid.

Full Text: PDF DOI: 10.5539/jmr.v5n4p39

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.

Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

Copyright © Canadian Center of Science and Education

To make sure that you can receive messages from us, please add the '' domain to your e-mail 'safe list'. If you do not receive e-mail in your 'inbox', check your 'bulk mail' or 'junk mail' folders.


doaj_logo_new_120 proquest_logo_120images_120.