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Trends in the Representation Theory of Finite Dimensional Algebras
Edited by: Edward L. Green, Virginia Polytechnic Institute and State University, Blacksburg, VA, and Birge Huisgen-Zimmermann, University of California, Santa Barbara, CA
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Contemporary Mathematics
1998; 356 pp; softcover
Volume: 229
ISBN-10: 0-8218-0928-8
ISBN-13: 978-0-8218-0928-0
List Price: US$91
Member Price: US$72.80
Order Code: CONM/229
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This refereed collection of research papers and survey articles reflects the interplay of finite-dimensional algebras with other areas (algebraic geometry, homological algebra, and the theory of quantum groups). Current trends are presented from the discussions at the AMS-IMS-SIAM Joint Summer Research Conference at the University of Washington (Seattle).

The volume features several excellent expository articles which will introduce the beginning researcher to cutting-edge topics in representation theory. The book will also provide inspiration to researchers in related areas, as it includes original papers spanning a broad spectrum of representation theory.

Features:

  • Work outlining significant progress on long-standing open problems.
  • Survey articles offering both overviews and introductions to various subfields of the topic.
  • Expositions reflecting the interplay between the representation theory of algebras and other fields.

Readership

Graduate students and researchers in representation theory of algebras, noetherian rings, Hopf algebras, quantum groups, deformation theory, applications of algebraic geometry and invariant theory to representation theory.

Table of Contents

  • I. Assem and F. U. Coelho -- Postprojective partitions for tilting torsion pairs
  • M. Barot and H. Lenzing -- Derived canonical algebras as one-point extensions
  • F. M. Bleher -- Special biserial algebras and their automorphisms
  • S. Brenner and M. C. R. Butler -- Wild subquivers of the Auslander-Reiten quiver of a tame algebra
  • K. A. Brown -- Representation theory of Noetherian Hopf algebras satisfying a polynomial identity
  • R.-O. Buchweitz -- Finite representation type and periodic Hochschild (co-)homology
  • M. C. R. Butler -- The syzygy theorem for monomial algebras
  • J. A. de la Peña -- Algebras whose derived category is tame
  • P. Dräxler -- Circular biextensions of tame concealed algebras
  • R. Farnsteiner -- On the distribution of AR-components of restricted Lie algebras
  • M. Gerstenhaber and A. Giaquinto -- Compatible deformations
  • D. Happel and I. Reiten -- Directing objects in hereditary categories
  • D. Happel and L. Unger -- On subcategories associated with tilting modules
  • Y. Iwanaga and J. Miyachi -- Modules of the highest homological dimension over a Gorenstein ring
  • M. Kauer -- Derived equivalence of graph algebras
  • O. Kerner -- Basic results on wild hereditary algebras
  • H. Krause and M. Saorín -- On minimal approximations of modules
  • R. Martínez-Villa -- Serre duality for generalized Auslander regular algebras
  • S. Montgomery -- Classifying finite-dimensional semisimple Hopf algebras
  • C. Riedtmann -- Geometry of modules: Degenerations
  • C. M. Ringel -- The preprojective algebra of a tame quiver: The irreducible components of the module varieties
  • D. Simson -- Representation types, Tits reduced quadratic forms and orbit problems for lattices over orders
  • A. Skowroński and G. Zwara -- Degenerations in module varieties with finitely many orbits
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