BIREP

### Compiled by C.M.Ringel

## Representation Theory of Algebras: Striking New Results

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

### Striking new examples:

- Peach (and Chuang): Rhombal algebras.
- 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

E-Mail:
ringel@mathematik.uni-bielefeld.de