Quadrics via Semigroups
Abstract
This is the story of the rediscovery of classical three-dimensional geometry, especially the geometry of quadric surfaces, while studying the semigroup M2( 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 spaghetti bundle in Samu:88. In this story the spaghetti presents itself as the set of idempotents in M2( 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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