Quantum Groups and Their Primitive Ideals
By: by Anthony Joseph
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge A Series of Modern Surveys in Mathematics -- 29; Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge A Series of Modern Surveys in Mathematics -- 29.
Publisher: Springer Berlin Heidelberg
Published: 1995
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 383
ISBN-13: 9783642784026; 9783642784002
Subjects: Mathematics; Geometry, algebraic; Topological Groups; Algebra
Description: The primary aim of this book is an in-depth study of the Drinfeld-Jimbo quantization Uq(g) of the enveloping algebra U(g) of a semisimple Lie algebra g and of the Hopf dual Rq (G) of Uq(g). The focus is on determining the primitive spectra of these rings. A systematic use of Hopf algebra structure, and in particular of adjoint action, is to be made. There will be an emphasis on "quantum phenomena" which are new features of Uq(g) and on how these can be used to even simplify the study of U(g). The reader will learn how the quantum viewpoint has revitalized the study of enveloping algebras and will become acquainted with proofs which have been developed over the last 20 years into a particularly efficient form. Many of the results are now only just being published in research journals.
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