Elimination orderings and localization in PBW algebras.

DOI10.1016/j.laa.2008.11.024zbMath1213.16039OpenAlexW2051954635MaRDI QIDQ1014479

F. J. Lobillo, Jesus García Miranda, Juan Ignacio García García

Publication date: 29 April 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2008.11.024

zbMATH Keywords

Weyl algebrasmonomial orderingsOre setsPBW algebrasquantum spacesquantum enveloping algebraselimination orderings

Mathematics Subject Classification ID

Commutative semigroups (20M14) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Computational aspects of associative rings (general theory) (16Z05) Ore rings, multiplicative sets, Ore localization (16U20) Associative rings of fractions and localizations (16S85)

Related Items

Modular techniques for noncommutative Gröbner bases ⋮ Computing diagonal form and Jacobson normal form of a matrix using Gröbner bases ⋮ Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases

Uses Software

• Plural
• SINGULAR
• nctools.lib

Cites Work

• Quantum groups at roots of 1
• Non-commutative Gröbner bases in algebras of solvable type
• A Poincaré-Birkhoff-Witt theorem for quantized universal enveloping algebras of type \(A_ N\)
• An extension of Buchberger's algorithm and calculations in enveloping fields of Lie algebras
• The diamond lemma for ring theory
• Noncommutative Gröbner bases and filtered-graded transfer.
• PRIMALITY TEST IN ITERATED ORE EXTENSIONS
• Intersection of ideals with non-commutative subalgebras
• Homological computations in PBW modules.
• Re-filtering and exactness of the Gelfand-Kirillov dimension
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