  Given a subshift over an arbitrary alphabet, we construct a representation of
the associated unital algebra. We describe a criteria for the faithfulness of
this representation in terms of the existence of cycles with no exits.
Subsequently, we focus on describing the irreducible components of this
representation and characterize equivalence between such components. Building
upon these findings, we identify the minimal left ideals of a subshift algebra
associated with (what we call) line paths.
