Classification of Four Dimensional Train Algebras of Degree 2 and Exponent 4

Abstract

This paper is devoted to the classification of train algebras of degree 2 and exponent 4. This classification is made in dimension at most four and according to the type of the algebra. We first show that in four dimension, the type of algebra can only be of (2,0,1,1), (2,1,0,1) or (2,1 ,1,0).