Gröbner bases in universal enveloping algebras of Leibniz algebras

DOI10.1016/j.jsc.2007.07.020zbMath1163.17004OpenAlexW2063408879WikidataQ123118129 ScholiaQ123118129MaRDI QIDQ1012142

Manuel Ladra Gonzalez, Manuel Avelino Insua Hermo

Publication date: 14 April 2009

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2007.07.020

zbMATH Keywords

Gröbner basesuniversal enveloping algebraLeibniz algebraPoincaré-Birkhoff-Witt theorem

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Leibniz algebras (17A32)

Related Items

Universal Associative Envelopes of (n+ 1)-Dimensionaln-Lie Algebras, On the definitions of nucleus for dialgebras, Test for Leibniz \(n\)-algebra structure

Uses Software

• Plural
• SINGULAR
• NCAlgebra

Cites Work

• Non-commutative Gröbner bases in algebras of solvable type
• An extension of Buchberger's algorithm and calculations in enveloping fields of Lie algebras
• The diamond lemma for ring theory
• Universal enveloping algebras of Leibniz algebras and (co)homology
• A noncommutative version of Lie algebras: Leibniz algebras
• An introduction to commutative and noncommutative Gröbner bases
• Noncommutative Gröbner bases and filtered-graded transfer.
• Gröbner bases for polynomial ideals over commutative regular rings
• On the finiteness of Gröbner bases computation in quotients of the free algebra.
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