Bessenrodt, Christine Algebra invariants for finite directed graphs with relations. (English) Zbl 1183.16014 Sémin. Lothar. Comb. 54A, B54Ag, 11 p. (2005). Summary: Finite directed graphs with relations define finite-dimensional algebras given as factor algebras of the corresponding path algebras. In joint work with T. Holm [Pac. J. Math. 229, No. 1, 25-47 (2007; Zbl 1160.16006)], we studied invariants of an associated generalized Cartan 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 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. MSC: 16G20 Representations of quivers and partially ordered sets 16E35 Derived categories and associative algebras 18E30 Derived categories, triangulated categories (MSC2010) Keywords:finite directed graphs; finite-dimensional algebras; path algebras; skewed-gentle algebras; generalized Cartan matrices; Cartan invariants; derived categories Citations:Zbl 1160.16006 PDFBibTeX XMLCite \textit{C. Bessenrodt}, Sémin. Lothar. Comb. 54A, B54Ag, 11 p. (2005; Zbl 1183.16014) Full Text: EuDML EMIS