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Séminaire Lotharingien de Combinatoire, B54Ag (2006), 11 pp.

# Christine Bessenrodt

# Algebra Invariants for Finite Directed Graphs
with Relations

**Abstract.**
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 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.

Received: December 15, 2005.
Accepted: October 14, 2006.
Final Version: October 16, 2006.

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