Dense Orbits of a Two Point Algebra

Abstract

Finite dimensional algebras over a field can be classified into three classes by representation type. These are finite, tame, and wild. Wild algebras contain copies of the representations of all finite dimensional algebras so classifying the indecomposable representations is not feasible. We then look at representations whose orbit is dense in their associated irreducible component of their representation variety. With this geometric perspective, we can approximate our representations. We give an example of a two point dense orbit algebra of wild representation type and show that it has a dense orbit for dimension vectors of certain types.