Quantum sections and Gauge algebras

Abstract

Using quantum sections of filtered rings and the associated Rees rings one can lift the scheme structure on Proj of the associated graded ring to the Proj of the Rees ring . The algebras of interest here are positively filtered rings having a non-commutative regular quadratic algebra for the associated graded ring ; these are the socalled gauge algebras obtaining their name from special examples appearing in E. Witten's gauge theories . The paper surveys basic definitions and properties but concentrates on the development of several concrete examples.