Examples and quantum sections of schematic algebras
In an earlier paper, [J. Pure Appl. Algebra 104, No. 1, 109-122 (1995; Zbl 0854.16027)], the authors developed their notion of a ``schematic algebra'', a (non-commutative) connected graded Noetherian \(k\)-algebra having a finite collection \(\{S_i\}\) of Ore sets such that a graded left ideal \(I\) with \(I\cap S_i\neq\emptyset\) for all \(i\) must contain a power of the augmentation ideal. They proposed this concept as providing a notion of scheme in the setting of non-commutative geometry. The purpose of the present paper is to provide examples of schematic algebras -- for example, the Rees rings of almost commutative rings, the coordinate ring of quantum \(2\times 2\) matrices, quantum Weyl algebras and the three dimensional Sklyanin algebra are shown to be schematic.
scientific article; zbMATH DE number 1067516
scientific article