Some algorithmic problems for Poisson algebras

DOI10.1016/j.jalgebra.2019.02.001zbMath1462.17024OpenAlexW2912289736WikidataQ128491390 ScholiaQ128491390MaRDI QIDQ1730211

Yuqun Chen, Zerui Zhang, Leonid A. Bokut'

Publication date: 11 March 2019

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2019.02.001

zbMATH Keywords

word problemPoisson algebraGröbner-Shirshov basis

Mathematics Subject Classification ID

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) Poisson algebras (17B63)

Related Items (3)

Defining relations and Gröbner–Shirshov bases of Poisson algebras as of conformal modules ⋮ Poisson triple systems ⋮ On the Special Identities of Gelfand–Dorfman Algebras

Cites Work

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• Universal enveloping algebras and universal derivations of Poisson algebras
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• Gröbner-Shirshov bases for Lie algebras: after A. I. Shirshov
• Quantization of Poisson superalgebras and speciality of Jordan Poisson superalgebras
• Differential type operators and Gröbner-Shirshov bases.
• Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Translation from the German
• The Freiheitssatz for Novikov algebras
• Centralizers in free Poisson algebras
• Gröbner–Shirshov bases and their calculation
• Free differential calculus. IV: The quotient groups of the lower central series

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