Examples and quantum sections of schematic algebras Original Research Article

In a previous paper, we defined schematic algebras as algebras having “enough” Ore-sets and developed a noncommutative scheme theory for them. The present paper is a sequel in which we prove a lifting properety for Ore-sets. This allows us to exhibit many examples of schematic algebras like homogenizations of almost commutative algebras. We use various techniques to show that other algebras like the three-dimensional Sklyanin algebras are schematic. We also calculate explicitly the quantum-sections of enveloping algebras and use local information (their one-dimensional representations) to determine the point modules.