arXiv subjects
Publications and source records attributed to K R Goodearl.
Tauvel's height formula, which provides a link between the height of a prime ideal and the Gelfand-Kirillov dimension of the corresponding factor algebra, is verified for quantum nilpotent algebras.
A uniqueness theorem for an LU decomposition of a totally nonnegative matrix is obtained.
Explicit generating sets are found for all primitive ideals in the generic quantized coordinate rings of the 3x3 special and general linear groups over an arbitrary algebraically closed field. (Previously, generators were only known up to certain localizations.) The generating sets form polynormal regular sequences, from which it follows that all primitive factor algebras of these quantized coordinate rings are Auslander-Gorenstein and Cohen-Macaulay.
A general method is developed for deriving Quantum First and Second Fundamental Theorems of Coinvariant Theory from classical analogs in Invariant Theory, in the case that the quantization parameter q is transcendental over a base field. Several examples are given illustrating the utility of the method; these recover earlier results of various researchers including Domokos, Fioresi, Hacon, Rigal, Strickland, and the present authors.