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On computation of minimal free resolutions over solvable polynomial algebras

Huishi Li — 2015

Commentationes Mathematicae Universitatis Carolinae

Let $A = K [a_{1}, ..., a_{n}]$ be a (noncommutative) solvable polynomial algebra over a field $K$ in the sense of A. Kandri-Rody and V. Weispfenning [Non-commutative 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) $A = ⨁_{p \in ℕ} A_{p}$ is an $ℕ$ -graded algebra with the degree-0 homogeneous part $A_{0} = K$ ; (2) $A$ is an $ℕ$ -filtered algebra with the filtration ${F_{p} A}_{p \in ℕ}$ determined by a positive-degree...

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