Chrysostomos Psaroudakis

Reduction Techniques for the Finitistic Dimension

Abstract:

One of the longstanding open problems in Representation Theory of Finite Dimensional Algebras is the so called "Finitistic Dimension Conjecture". The latter homological conjecture is known to be related with other important problems concerning the homological behaviour and the structure theory of finite dimensional algebras. Our aim in this talk is to present some reduction techniques for the finitistic dimension. In particular, we will show that we can remove some vertices and some arrows from a quotient of a path algebra such that the problem of computing the finitistic dimension can be reduced to a possible simpler ("homologically compact") algebra. The results will be illustrated with examples. This is joint work with Edward L. Green and Øyvind Solberg.