Conference abstracts

Session S11 - Representations of Algebras

July 26, 18:00 ~ 18:20

## About sums of compositions of irreducible morphisms

### Nicolás Llodra Schat

### Universidad Nacional de Mar del Plata, Argentina - nllodra@gmail.com

We consider $A$ an artin algebra, and $\mbox{mod}\,A$ the category of finitely generated right $A$-modules.

In this talk, we present some results about sums of compositions of irreducible morphisms between indecomposable $A$-modules in relation with the powers of the radical of its module category.

The notion of degree of an irreducible morphism, introduced by S. Liu [L], played a fundamental role to obtain such results.

In particular, we give a characterization of when the sums of compositions of irreducible morphisms of length exactly $n$, for $n=2,3,4$ and $5$ belong to $\Re^{n+1}$.

\vspace{.1in} \textbf{References} \vspace{.1in}

[L] S. Liu, {\it Degree of irreducible maps and the shapes of Auslander-Reiten quivers}, Journal of London Math. Soc. 2, 45, (1992), 32-54.

Joint work with Claudia Chaio (Universidad Nacional de Mar del Plata, Argentina).