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On the Spectra of Quantum Groups
 
Milen Yakimov Louisiana State University, Baton Rouge, Louisiana
On the Spectra of Quantum Groups
eBook ISBN:  978-1-4704-1532-7
Product Code:  MEMO/229/1078.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $42.60
On the Spectra of Quantum Groups
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On the Spectra of Quantum Groups
Milen Yakimov Louisiana State University, Baton Rouge, Louisiana
eBook ISBN:  978-1-4704-1532-7
Product Code:  MEMO/229/1078.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $42.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2292013; 91 pp
    MSC: Primary 16; Secondary 20; 17; 53;

    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 centers of certain localizations of quotients of \(R_q[G]\) by torus invariant prime ideals, or equivalently in terms of orbits of finite groups. These centers were only known up to finite extensions. The author determines the centers 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 parametrization of \(\mathrm{Spec} R_q[G]\).

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Previous results on spectra of quantum function algebras
    • 3. A description of the centers of Joseph’s localizations
    • 4. Primitive ideals of $R_q[G]$ and a Dixmier map for $R_q[G]$
    • 5. Separation of variables for the algebras $S^\pm _w$
    • 6. A classification of the normal and prime elements of the De Concini–Kac–Procesi algebras
    • 7. Module structure of $R_{\mathbf {w}}$ over their subalgebras generated by Joseph’s normal elements
    • 8. A classification of maximal ideals of $R_q[G]$ and a question of Goodearl and Zhang
    • 9. Chain properties and homological applications
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2292013; 91 pp
MSC: Primary 16; Secondary 20; 17; 53;

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 centers of certain localizations of quotients of \(R_q[G]\) by torus invariant prime ideals, or equivalently in terms of orbits of finite groups. These centers were only known up to finite extensions. The author determines the centers 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 parametrization of \(\mathrm{Spec} R_q[G]\).

  • Chapters
  • 1. Introduction
  • 2. Previous results on spectra of quantum function algebras
  • 3. A description of the centers of Joseph’s localizations
  • 4. Primitive ideals of $R_q[G]$ and a Dixmier map for $R_q[G]$
  • 5. Separation of variables for the algebras $S^\pm _w$
  • 6. A classification of the normal and prime elements of the De Concini–Kac–Procesi algebras
  • 7. Module structure of $R_{\mathbf {w}}$ over their subalgebras generated by Joseph’s normal elements
  • 8. A classification of maximal ideals of $R_q[G]$ and a question of Goodearl and Zhang
  • 9. Chain properties and homological applications
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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