The Points of Quadratic Algebras


Michaela Vancliff


Abstract: I plan to present recent joint work by Brad Shelton and myself, with emphasis on the following counter-intuitive result. Let A denote a non-commutative algebra on four generators with six defining relations (each homogeneous of degree 2), and let Z denote the locus of zeros of the defining relations of A. If Z is finite, then the space of (1,1)-forms that vanish on Z is the span of the defining relations of A. The result concerns the ``points'' of A and has a counterpart involving ``lines'' of A. Although the results are non-commutative in nature, the proofs use only commutative algebra.


created Thu Jun 1 13:07:48 PDT 2000