Compiled by C.M.Ringel

Representation Theory of Algebras: Striking New Results

  1. Zwara: An algebraic description of degeneration
  2. Happel: The hereditary categories with tilting object are the known ones.
  3. Enochs: Proof of the flat cover conjecture.
  4. Iyama: The representation dimension of an algebra is finite
  5. Igusa-Todorov: Every algebra with representation dimension at most 3 has finite finitistic dimension.
  6. Rouqier: The representation dimension of the exterior algebra of an n-dimensional vector space is n+1.
  7. Buan, Marsh, Reiten (and others): Cluster-tilted algebras

Striking new examples:

  1. Peach (and Chuang): Rhombal algebras.
  2. Muro: A triangulated category which is not algebraic (not even topological)

Some mathematicians have complained that this list is still quite short. It has to be asserted that there has been a tremendous amount of results which are interesting or important (or even both), the Beijing conference 2000 gave clear evidence, see also the monthly lists which are available in fdlist - New Papers. However, the aim of this page with the title Striking New Results is to draw attention to results which are really striking, thus either solutions to long-standing and decisive questions (thus Zimmermann-Huisgen's example that the small and the large finitistic dimensions may differ, would have qualified in this contest) or else surprising observations which provide a completely new insight (again an older example: the existence of the Kerner bijections for wild quiver algebras). Of course, all mathematicians are encouraged to propose entries for this list.
Begin: 14.2.1998. Updated: 26.05.2002
Fakultät für Mathematik, Universität Bielefeld, C.M.Ringel