Tuesday, January 16, 14:00, 7.527
Reduction Techniques for the Finitistic Dimension
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.