Geodesic
On computation of minimal free resolutions over solvable polynomial algebras
Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 4, pp. 447-503.

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Let $A=K[a_1,\ldots ,a_n]$ 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) $A=\bigoplus_{p\in\mathbb{N}}A_p$ is an $\mathbb{N}$-graded algebra with the degree-0 homogeneous part $A_0=K$; (2) $A$ is an $\mathbb{N}$-filtered algebra with the filtration $\{F_pA\}_{p\in\mathbb{N}}$ determined by a positive-degree function on $A$.
DOI : 10.14712/1213-7243.2015.141
Classification : 16W70, 16Z05
Keywords: solvable polynomial algebra; Gröbner basis; minimal free resolution 
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     title = {On computation of minimal free resolutions over solvable polynomial algebras},
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Li, Huishi. On computation of minimal free resolutions over solvable polynomial algebras. Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 4, pp. 447-503. doi : 10.14712/1213-7243.2015.141. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.141/

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