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JOURNALS // Algebra and Discrete Mathematics // Archive

Algebra Discrete Math., 2007 Issue 1, Pages 24–39 (Mi adm185)

RESEARCH ARTICLE

On Frobenius full matrix algebras with structure systems

Hisaaki Fujitaa, Yosuke Sakaia, Daniel Simsonb

a Institute of Mathematics, University of Tsukuba, Ibaraki 305–8571
b Faculty of Mathematics and Computer Sciences, Nicolaus Copernicus University, 87–100 Toruń, Poland

Abstract: 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, module, socle, tame representation type.

MSC: 16G10, 16G30, 16G60

Received: 29.10.2006
Revised: 28.05.2007

Language: English



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