On the Anick-Green Resolution and Computations over Quotient of Path Algebras

Abstract

Our goal is to understand the computation of a projective resolution for simple modules over homomorphic images of path algebras. We provide an algorithmic way to compute the differential and the projective resolution. Our work includes a software package PathAlgebras for the computer algebra system Macaulay2 with the functionality to compute Gröbner Basis, syzygies, projective resolutions, Betti tables of simple modules, and other important information over quotients of path algebras.