On the spectra of quantum groups / Milen Yakimov.

Format:

Book

Author/Creator:

Yakimov, Milen, 1973- author.

Series:

Memoirs of the American Mathematical Society ; Volume 229, Number 1078.

Memoirs of the American Mathematical Society, 1947-6221 ; Volume 229, Number 1078

Language:

English

Subjects (All):

Quantum groups.

Physical Description:

1 online resource (104 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2013.

Language Note:

English

Summary:

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] .

Contents:

""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Previous results on spectra of quantum function algebras""; ""2.1. Quantized universal enveloping algebras""; ""2.2. Type 1 modules and braid group action""; ""2.3. -prime ideals of Quantum Groups""; ""2.4. Sets of normal elements""; ""2.5. Localizations of quotients of _{ }[ ] by its -primes""; ""2.6. Spectral decomposition theorem for _{ }[ ]""; ""2.7. The De Concini�Kac�Procesi algebras""; ""2.8. A second presentation of ^{ }_{±}""; ""Chapter 3. A description of the centers of Joseph�s localizations""

""7.4. Structure of the algebras �_{ } and separation of variables for _{ }""""7.5. Structure of the algebras _{ } and freeness of _{ } over _{ }""; ""Chapter 8. A classification of maximal ideals of _{ }[ ] and a question of Goodearl and Zhang""; ""8.1. A projection property of the ideal _{(1,1)}""; ""8.2. Proof of \prref{PROJJ}""; ""8.3. Proof of \thref{MAX}""; ""8.4. Classification of _{ }[ ] and a question of Goodearl and Zhang""; ""Chapter 9. Chain properties and homological applications""; ""9.1. Applications""

Notes:

"Volume 229, Number 1078 (fifth of 5 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-1532-1