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.

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

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