On the Spectra of Quantum Groups

ISBN-13: 9780821891742 / Angielski

Milen Yakimov

Opis

Joseph and Hodges-Levasseur (in the A case) described the spectra of all quantum function algebras R q [G] on simple algebraic groups in terms of the centres of certain localisations of quotients of R q [G] by torus invariant prime ideals, or equivalently in terms of orbits of finite groups. These centres were only known up to finite extensions. The author determines the centres explicitly under the general conditions that the deformation parameter is not a root of unity and without any restriction on the characteristic of the ground field. From it he deduces a more explicit description of all prime ideals of R q [G] than the previously known ones and an explicit parametrisation of SpecR q [G] .

Spis treści

• Introduction
• Previous results on spectra of quantum function algebras
• A description of the centers of Joseph's localizations
• Primitive ideals of R q [G] and a Dixmier map for R q [G]
• Separation of variables for the algebras S ± w
• A classification of the normal and prime elements of the De Concini-Kac-Procesi algebras
• Module structure of R w over their subalgebras generated by Joseph's normal elements
• A classification of maximal ideals of R q [G] and a question of Goodearl and Zhang
• Chain properties and homological applications
• Bibliography