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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, and Claus Michael Ringel, Universität Bielefeld, Germany
A co-publication of the AMS and Fields Institute.
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Fields Institute Communications
2004; 479 pp; hardcover
Volume: 40
ISBN-10: 0-8218-3416-9
ISBN-13: 978-0-8218-3416-9
List Price: US$131
Member Price: US$104.80
Order Code: FIC/40
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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
  • K. S. Brown -- Semigroup and ring theoretical methods in probability
  • T. Bruestle -- Typical examples of tame algebras
  • O. Iyama -- Representation dimension and Solomon zeta function
  • S. Koenig -- Filtrations, stratifications and applications
  • M. S. Putcha -- Bruhat-Renner decomposition and Hecke algebras of reductive monoids
  • L. E. Renner -- Representations and blocks of algebraic monoids
  • M. Schocker -- The descent algebra of the symmetric group
Specialized Workshop Commutative Algebra, Algebraic Geometry and Representation Theory
  • Y. Berest -- A remark on Letzter-Makar-Limanov invariants
  • I. Burban -- Derived categories of coherent sheaves on rational singular curves
  • Y. A. Drozd -- Vector bundles and Cohen-Macaulay modules
Specialized Workshop Finite Dimensional Algebras, Algebraic Groups and Lie Theory
  • J. Du -- Finite dimensional algebras, quantum groups and finite groups of Lie type
  • V. Mazorchuk -- Stratified algebras arising in Lie theory
  • T. Tanisaki -- Character formulas of Kazhdan-Lusztig type
  • P. Webb -- Weight theory in the context of arbitrary finite groups
Specialized Workshop Quantum Groups and Hall Algebras
  • G. Benkart and S. Witherspoon -- Restricted two-parameter quantum groups
  • B. Deng and J. Xiao -- On Ringel-Hall algebras
  • Z. Lin -- Lusztig's geometric approach to Hall algebras
  • M. Reineke -- The use of geometric and quantum group techniques for wild quivers
  • K. Rietsch -- An introduction to perverse sheaves
  • Y. Saito -- An introduction to canonical bases
  • O. Schiffmann -- Quivers of type \(A\), flag varieties and representation theory
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