On computation of minimal free resolutions over solvable polynomial algebras

Let A = K[a1, . . . , an] be a (noncommutative) solvable polynomial algebra over a field K in the sense of A. Kandri-Rody and V. Weispfenning [Noncommutative Gröbner bases in algebras of solvable type, J. Symbolic Comput. 9 (1990), 1-26]. This paper presents a comprehensive study on the computation of minimal free resolutions of modules over A in the following two cases: (1) A = ⊕pεN Ap is an N-graded algebra with the degree-0 homogeneous part A0 = K; (2) A is an N-filtered algebra with the filtration (FpA)pεN determined by a positive-degree function on A.