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Stratifying Endomorphism Algebras
 
Edward Cline University of Oklahoma, Norman, OK
Brian Parshall University of Virginia, Charlottesville, VA
Leonard Scott University of Virginia, Charlottesville, VA
Stratifying Endomorphism Algebras
eBook ISBN:  978-1-4704-0176-4
Product Code:  MEMO/124/591.E
List Price: $46.00
MAA Member Price: $41.40
AMS Member Price: $27.60
Stratifying Endomorphism Algebras
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Stratifying Endomorphism Algebras
Edward Cline University of Oklahoma, Norman, OK
Brian Parshall University of Virginia, Charlottesville, VA
Leonard Scott University of Virginia, Charlottesville, VA
eBook ISBN:  978-1-4704-0176-4
Product Code:  MEMO/124/591.E
List Price: $46.00
MAA Member Price: $41.40
AMS Member Price: $27.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1241996; 119 pp
    MSC: Primary 16; 20; 17;

    Suppose that \(R\) is a finite dimensional algebra and \(T\) is a right \(R\)-module. Let \(A = \mathrm{ End}_R(T)\) be the endomorphism algebra of \(T\). This memoir presents a systematic study of the relationships between the representation theories of \(R\) and \(A\), especially those involving actual or potential structures on \(A\) which ”stratify” its homological algebra. The original motivation comes from the theory of Schur algebras and the symmetric group, Lie theory, and the representation theory of finite dimensional algebras and finite groups.

    The book synthesizes common features of many of the above areas, and presents a number of new directions. Included are an abstract ”Specht/Weyl module” correspondence, a new theory of stratified algebras, and a deformation theory for them. The approach reconceptualizes most of the modular representation theory of symmetric groups involving Specht modules and places that theory in a broader context. Finally, the authors formulate some conjectures involving the theory of stratified algebras and finite Coexeter groups, aiming toward understanding the modular representation theory of finite groups of Lie type in all characteristics.

    Readership

    Graduate students and research mathematicians interested in representation theory of algebraic and finite groups, finite-dimensional algebras, and Lie algebras.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. Preliminaries
    • 2. Stratified algebras
    • 3. Stratifying endomorphism algebras
    • 4. Stratifications and orders in semisimple algebras
    • 5. Examples
    • 6. Some conjectures for finite Coxeter groups and further remarks
  • 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: 1241996; 119 pp
MSC: Primary 16; 20; 17;

Suppose that \(R\) is a finite dimensional algebra and \(T\) is a right \(R\)-module. Let \(A = \mathrm{ End}_R(T)\) be the endomorphism algebra of \(T\). This memoir presents a systematic study of the relationships between the representation theories of \(R\) and \(A\), especially those involving actual or potential structures on \(A\) which ”stratify” its homological algebra. The original motivation comes from the theory of Schur algebras and the symmetric group, Lie theory, and the representation theory of finite dimensional algebras and finite groups.

The book synthesizes common features of many of the above areas, and presents a number of new directions. Included are an abstract ”Specht/Weyl module” correspondence, a new theory of stratified algebras, and a deformation theory for them. The approach reconceptualizes most of the modular representation theory of symmetric groups involving Specht modules and places that theory in a broader context. Finally, the authors formulate some conjectures involving the theory of stratified algebras and finite Coexeter groups, aiming toward understanding the modular representation theory of finite groups of Lie type in all characteristics.

Readership

Graduate students and research mathematicians interested in representation theory of algebraic and finite groups, finite-dimensional algebras, and Lie algebras.

  • Chapters
  • Introduction
  • 1. Preliminaries
  • 2. Stratified algebras
  • 3. Stratifying endomorphism algebras
  • 4. Stratifications and orders in semisimple algebras
  • 5. Examples
  • 6. Some conjectures for finite Coxeter groups and further remarks
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
Please select which format for which you are requesting permissions.