Irreducible Representations of Power-associative Train Algebras

Author:

Behn Antonio1,Labra Alicia1,Reyes Cristián2

Affiliation:

1. Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653 Santiago, Chile

2. Centro de Modelamiento Matemático, Universidad de Chile, Casilla 170 Correo 3 Santiago, Chile

Abstract

Train algebras were introduced by Etherington in 1939 as an algebraic framework for treating genetic problems. The aim of this paper is to study the representations and irreducible representations of power-associative train algebras of rank 4. There are three families of such algebras and for two of them we prove that every irreducible representation has dimension one over the ground field. For the third family we give an example of an irreducible representation of dimension three.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

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