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Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry
 
Edited by: Vlastimil Dlab Carleton University, Ottawa, ON, Canada
Claus Michael Ringel Universität Bielefeld, Bielefeld, Germany
A co-publication of the AMS and Fields Institute
Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry
Hardcover ISBN:  978-0-8218-3416-9
Product Code:  FIC/40
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
eBook ISBN:  978-1-4704-3074-0
Product Code:  FIC/40.E
List Price: $145.00
MAA Member Price: $130.50
AMS Member Price: $116.00
Hardcover ISBN:  978-0-8218-3416-9
eBook: ISBN:  978-1-4704-3074-0
Product Code:  FIC/40.B
List Price: $300.00 $227.50
MAA Member Price: $270.00 $204.75
AMS Member Price: $240.00 $182.00
Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry
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Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry
Edited by: Vlastimil Dlab Carleton University, Ottawa, ON, Canada
Claus Michael Ringel Universität Bielefeld, Bielefeld, Germany
A co-publication of the AMS and Fields Institute
Hardcover ISBN:  978-0-8218-3416-9
Product Code:  FIC/40
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
eBook ISBN:  978-1-4704-3074-0
Product Code:  FIC/40.E
List Price: $145.00
MAA Member Price: $130.50
AMS Member Price: $116.00
Hardcover ISBN:  978-0-8218-3416-9
eBook ISBN:  978-1-4704-3074-0
Product Code:  FIC/40.B
List Price: $300.00 $227.50
MAA Member Price: $270.00 $204.75
AMS Member Price: $240.00 $182.00
  • Book Details
     
     
    Fields Institute Communications
    Volume: 402004; 479 pp
    MSC: Primary 16; 17; 14; Secondary 05; 13; 15; 18; 20; 51; 81;

    These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional “instructional” workshop preceding the conference, there were also workshops on “Commutative Algebra, Algebraic Geometry and Representation Theory”, “Finite Dimensional Algebras, Algebraic Groups and Lie Theory”, and “Quantum Groups and Hall Algebras”. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated.

    The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented.

    The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions.

    The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases.

    The book is recommended for graduate students and researchers in algebra and geometry.

    Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

    Readership

    Graduate students and research mathematicians interested in representations of finite-dimensional algebras and applications.

  • Table of Contents
     
     
    • Instructional Workshop
    • Kenneth Brown — Semigroup and ring theoretical methods in probability
    • Thomas Bruestle — Typical examples of tame algebras
    • Osamu Iyama — Representation dimension and Solomon zeta function
    • Steffen Koenig — Filtrations, stratifications and applications
    • Mohan Putcha — Bruhat-Renner decomposition and Hecke algebras of reductive monoids
    • Lex Renner — Representations and blocks of algebraic monoids
    • Manfred Schocker — The descent algebra of the symmetric group
    • Specialized Workshop Commutative Algebra, Algebraic Geometry and Representation Theory
    • Yuri Berest — A remark on Letzter–Makar-Limanov invariants
    • Igor Burban — Derived categories of coherent sheaves on rational singular curves
    • Yuriy Drozd — Vector bundles and Cohen-Macaulay modules
    • Specialized Workshop Finite Dimensional Algebras, Algebraic Groups and Lie Theory
    • Jie Du — Finite dimensional algebras, quantum groups and finite groups of Lie type
    • Volodymyr Mazorchuk — Stratified algebras arising in Lie theory
    • Toshiyuki Tanisaki — Character formulas of Kazhdan-Lusztig type
    • Peter Webb — Weight theory in the context of arbitrary finite groups
    • Specialized Workshop Quantum Groups and Hall Algebras
    • Georgia Benkart and Sarah Witherspoon — Restricted two-parameter quantum groups
    • Bangming Deng and Jie Xiao — On Ringel-Hall algebras
    • Zongzhu Lin — Lusztig’s geometric approach to Hall algebras
    • Markus Reineke — The use of geometric and quantum group techniques for wild quivers
    • Konstanze Rietsch — An introduction to perverse sheaves
    • Yoshihisa Saito — An introduction to canonical bases
    • Olivier Schiffmann — Quivers of type $A$, flag varieties and representation theory
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 402004; 479 pp
MSC: Primary 16; 17; 14; Secondary 05; 13; 15; 18; 20; 51; 81;

These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional “instructional” workshop preceding the conference, there were also workshops on “Commutative Algebra, Algebraic Geometry and Representation Theory”, “Finite Dimensional Algebras, Algebraic Groups and Lie Theory”, and “Quantum Groups and Hall Algebras”. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated.

The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented.

The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions.

The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases.

The book is recommended for graduate students and researchers in algebra and geometry.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Graduate students and research mathematicians interested in representations of finite-dimensional algebras and applications.

  • Instructional Workshop
  • Kenneth Brown — Semigroup and ring theoretical methods in probability
  • Thomas Bruestle — Typical examples of tame algebras
  • Osamu Iyama — Representation dimension and Solomon zeta function
  • Steffen Koenig — Filtrations, stratifications and applications
  • Mohan Putcha — Bruhat-Renner decomposition and Hecke algebras of reductive monoids
  • Lex Renner — Representations and blocks of algebraic monoids
  • Manfred Schocker — The descent algebra of the symmetric group
  • Specialized Workshop Commutative Algebra, Algebraic Geometry and Representation Theory
  • Yuri Berest — A remark on Letzter–Makar-Limanov invariants
  • Igor Burban — Derived categories of coherent sheaves on rational singular curves
  • Yuriy Drozd — Vector bundles and Cohen-Macaulay modules
  • Specialized Workshop Finite Dimensional Algebras, Algebraic Groups and Lie Theory
  • Jie Du — Finite dimensional algebras, quantum groups and finite groups of Lie type
  • Volodymyr Mazorchuk — Stratified algebras arising in Lie theory
  • Toshiyuki Tanisaki — Character formulas of Kazhdan-Lusztig type
  • Peter Webb — Weight theory in the context of arbitrary finite groups
  • Specialized Workshop Quantum Groups and Hall Algebras
  • Georgia Benkart and Sarah Witherspoon — Restricted two-parameter quantum groups
  • Bangming Deng and Jie Xiao — On Ringel-Hall algebras
  • Zongzhu Lin — Lusztig’s geometric approach to Hall algebras
  • Markus Reineke — The use of geometric and quantum group techniques for wild quivers
  • Konstanze Rietsch — An introduction to perverse sheaves
  • Yoshihisa Saito — An introduction to canonical bases
  • Olivier Schiffmann — Quivers of type $A$, flag varieties and representation theory
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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