An example of Bernstein duality
The authors show a local duality on \(K\)-algebras satisfying some algebraic properties, like the Auslander-Gorenstein property, the condition to be Cohen-Macaulay and the coincidence of injective and Gelfand-Kirillov dimensions. This local duality is a non-commutative version of local duality on commutative Gorenstein rings. In the known cases of enveloping algebras of finite-dimensional solvable Lie algebras and some of their extensions the codimension of cofinite prime ideals was \(1\). In the first part of the paper the authors develop the theory and obtain a characterization of local dualities. In the second one they introduce some examples of non-commutative algebras having a local duality. Among these examples, extra attention is paid to the quantum plane, because it provides examples of \(K\)-algebras in which the codimension of the cofinite prime ideals is greater than one.
scientific article; zbMATH DE number 1496429
scientific article