The Representation Type of Algebras and Subalgebras

Abstract

For A an associative algebra with identity over a field K, [A : K] < ∞, and d an integer, we define g _Λ(d) to be the number of inequivalent indecomposable Λ-modules of degree d over K. Following (6), we define Λ to be of finite representation type if . Λis said to be of bounded representation type if there exists d ₀ such that g _Λ(d) = 0 for d ⩾ d ₀; Λ is of unbounded representation type if not of bounded type.