Degree bounds for Gröbner bases in algebras of solvable type |
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Authors: | Matthias Aschenbrenner Anton Leykin |
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Affiliation: | a Department of Mathematics, University of California, Los Angeles, Box 951555, Los Angeles, CA 90095-1555, USA b Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street (M/C 249), Chicago, IL 60607-7045, USA |
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Abstract: | We establish doubly-exponential degree bounds for Gröbner bases in certain algebras of solvable type over a field (as introduced by Kandri-Rody and Weispfenning). The class of algebras considered here includes commutative polynomial rings, Weyl algebras, and universal enveloping algebras of finite-dimensional Lie algebras. For the computation of these bounds, we adapt a method due to Dubé based on a generalization of Stanley decompositions. Our bounds yield doubly-exponential degree bounds for ideal membership and syzygies, generalizing the classical results of Hermann and Seidenberg (in the commutative case) and Grigoriev (in the case of Weyl algebras). |
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Keywords: | Primary, 13P10, 13N10 secondary, 68Q40, 16S32 |
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