Minimal resolutions of algebras

M.C.R. Butler and A.D. King

Abstract. A method is described for constructing the minimal projective
resolution of an algebra considered as a bimodule over itself. The method
applies to an algebra presented as the quotient of a tensor algebra over a
separable algebra by an ideal of relations which is either homogeneous or
admissible (with some additional finiteness restrictions in the latter case).
In particular, it applies to any finite dimensional algebra over an 
algebraically closed field. The method is illustrated by a number of examples,
viz. truncated algebras, monomial algebras and Koszul algebras, with the aim
of unifying existing treatments of these in the literature.