Some characterisations of toupie algebras

DALIA ARTENSTEIN, MARIA ANDREA GATICA, MARCELO LANZILOTTA

Sherbrooke

Encuentro; XXIV Meeting on Representation Theory of Algebras; 2012

Universite de Sherbrooke

The goal of this talk is describe a family of finite dimensional algebras, called emph{toupie algebras}, that are a generalisation of the canonical algebras introduced by Ringel in 1984. More precisely, we study the simple connectedness, rigidity and representation type using combinatorial parameters associated to their quivers. In the first part of this talk, we computed the Hochschild cohomology groups of toupie algebras. Then we will see how these groups are useful to determine the simple connectedness and rigidity of them. In the second part, we determine the representation type of toupie algebras. medskip [AG] Artenstein, D.; Gatica {it Representation type of toupie algebras}, prepint. [CDHL] D. Castonguay, J. Dionne, F. Huard, M. Lanzilotta, {it Toupie algebras, some examples of laura algebras}, sometido 2010, arXiv:1011.5136v1. [GL] Gatica, M. A., Lanzilotta, M., {it Hochschild cohomology of a generalisation of canonical algebras}, prepint. [R] Ringel, C.M., Tame algebras and integral quadratic forms, Lecture Notes in Mathematics, 1099, Springer-Verlag, Berlin, 1984.