Representation dimension via tilting theory

Let Λ be an artin algebra over a commutative artinian ring R and let T be a separating-splitting tilting Λ-module with endomorphism Γ=EndΛ(T). The aim of this paper is to use tilting theory to study the representation dimension of Γ. The main result asserts that, for an integer n≥1, if Λ is n-Gorenstein of finite Cohen-Macaulay type, then rep.dim(Γ)≤n+2. We conclude that if Λ is a n-Gorenstein artin algebra of finite Cohen-Macaulay type, then rep.dim(Λ)≤n+2. This in particular shows that for any artin algebra Λ, rep.dim(Λ)≤gl.dim(Λ)+2.