| Abstract:
In a series of papers (which eventually blossomed into a Monograph
called "Cubic Forms"), the famous Russian algebraic geometer Ju. I.
Manin examined higher dimensional analogues of the familiar addition
law on a plane cubic curve. Unlike the planar case, the resulting
higher dimensional algebras are not groups. Instead, Manin managed to
prove that these cubic surfaces admit a commutative Moufang loop
structure (under an "admissible" equivalence relation). In this talk,
we give a representation theorem for Manin's "CH-quasigroups" and
illustrate the free algebra on two generators as a planar diagram of
tangentials of a cubic curve in the real projective plane.
|
