Quadrics via Semigroups

Details Quadrics via Semigroups Quadrics via Semigroups

2009-02-25

arxiv.org/abs/0902.4288v1

Mathematics

Rings and Algebras

6 pages

Scientific paper

This is the story of the rediscovery of classical three-dimensional geometry, especially the geometry of quadric surfaces, while studying the semigroup $M_2(\mathbb R)$ of linear endomorphisms of a real plane. One of the surfaces that appears prominently in this context is the hyperboloid of one sheet, referred to as {\em spaghetti bundle} in \cite{Samu:88}. In this story the spaghetti presents itself as the set of idempotents in $M_2(\mathbb R)$, the cone emerges as the set of nilpotent elements and the hyperbolic paraboloid as the set of semigroup-theoretic inverses of a singular element.

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