Article B54Ag

Christine Bessenrodt
2006 Séminaire Lotharingien de Combinatoire   unpublished
Finite directed graphs with relations define finite-dimensional algebras given as factor algebras of the corresponding path algebras. In joint work with T. Holm, we studied invariants of an associated generalized Car-tan matrix for certain types of algebras where the Cartan invariants basically count nonzero paths; the main motivation for this came from the context of derived module categories and derived invariants. For the so-called (skewed) gentle algebras we computed explicit combinatorial
more » ... icit combinatorial formulae for the invariant factors of the Cartan matrices. Based on the talk at the FPSAC'05 conference in Taormina, some of this work is surveyed here, and some further results on algebras of a different type are presented in the final section.