Geodesic
On Frobenius full matrix algebras with structure systems
Algebra and discrete mathematics, no. 1 (2007), pp. 24-39

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $n\geq 2$ 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.
Keywords: Frobenius algebra, quiver, tame representation type.
Mots-clés : module, socle 
@article{ADM_2007_1_a2,
     author = {Hisaaki Fujita and Yosuke Sakai and Daniel Simson},
     title = {On {Frobenius} full matrix algebras with structure systems},
     journal = {Algebra and discrete mathematics},
     pages = {24--39},
     publisher = {mathdoc},
     number = {1},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2007_1_a2/}
}
TY  - JOUR
AU  - Hisaaki Fujita
AU  - Yosuke Sakai
AU  - Daniel Simson
TI  - On Frobenius full matrix algebras with structure systems
JO  - Algebra and discrete mathematics
PY  - 2007
SP  - 24
EP  - 39
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2007_1_a2/
LA  - en
ID  - ADM_2007_1_a2
ER  - 
%0 Journal Article
%A Hisaaki Fujita
%A Yosuke Sakai
%A Daniel Simson
%T On Frobenius full matrix algebras with structure systems
%J Algebra and discrete mathematics
%D 2007
%P 24-39
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2007_1_a2/
%G en
%F ADM_2007_1_a2
Hisaaki Fujita; Yosuke Sakai; Daniel Simson. On Frobenius full matrix algebras with structure systems. Algebra and discrete mathematics, no. 1 (2007), pp. 24-39. http://geodesic.mathdoc.fr/item/ADM_2007_1_a2/