On Frobenius full matrix algebras with structure systems

Hisaaki Fujita ; Yosuke Sakai ; Daniel Simson

Algebra and discrete mathematics, no. 1 (2007), pp. 24-39.

Résumé

Let $n\ge 2$ be an integer. In [5] and [6], an $n\times n$ $\mathbb{A}$-full matrix algebra over a field $K$ is defined to be the set ${\mathbb{M}}_n(K)$ of all square $n\times n$ matrices with coefficients in $K$ equipped with a multiplication defined by a structure system $\mathbb{A}$, that is, an $n$-tuple of $n\times n$ matrices with certain properties. In [5] and [6], mainly $\mathbb{A}$-full matrix algebras having (0,1)-structure systems are studied, that is, the structure systems $\mathbb{A}$ such that all entries are 0 or 1. In the present paper we study $\mathbb{A}$-full matrix algebras having non (0,1)-structure systems. In particular, we study the Frobenius $\mathbb{A}$-full matrix algebras. Several infinite families of such algebras with nice properties are constructed in Section 4.

Détail

Keywords: Frobenius algebra, quiver, tame representation type.
Mots-clés : module, socle