On computation of minimal free resolutions over solvable polynomial algebras

Huishi Li

Commentationes Mathematicae Universitatis Carolinae (2015)

  • Volume: 56, Issue: 4, page 447-503
  • ISSN: 0010-2628

Abstract

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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 ∈ 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 ∈ ℕ determined by a positive-degree function on A .

How to cite

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Li, Huishi. "On computation of minimal free resolutions over solvable polynomial algebras." Commentationes Mathematicae Universitatis Carolinae 56.4 (2015): 447-503. <http://eudml.org/doc/276277>.

@article{Li2015,
abstract = {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 $\lbrace F_pA\rbrace _\{p\in \mathbb \{N\}\}$ determined by a positive-degree function on $A$.},
author = {Li, Huishi},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {solvable polynomial algebra; Gröbner basis; minimal free resolution},
language = {eng},
number = {4},
pages = {447-503},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On computation of minimal free resolutions over solvable polynomial algebras},
url = {http://eudml.org/doc/276277},
volume = {56},
year = {2015},
}

TY - JOUR
AU - Li, Huishi
TI - On computation of minimal free resolutions over solvable polynomial algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 4
SP - 447
EP - 503
AB - 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 $\lbrace F_pA\rbrace _{p\in \mathbb {N}}$ determined by a positive-degree function on $A$.
LA - eng
KW - solvable polynomial algebra; Gröbner basis; minimal free resolution
UR - http://eudml.org/doc/276277
ER -

References

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