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TitleGröbner bases in universal enveloping algebras of Leibniz algebras
Author(s) Manuel A. Insua, Manuel Ladra
TypeArticle in Journal
AbstractWe give a proof of the Poincaré–Birkhoff–Witt theorem for universal enveloping algebras of finite dimensional Leibniz algebras using Gröbner bases in a free associative algebra. We also construct Gröbner bases for two-sided ideals in universal enveloping algebras using the concept of Factor-Gröbner basis introduced by Nordbeck [Nordbeck, P., 2001. On the finiteness of Gröbner bases computation in quotients of the free algebra. Appl. Algebra Engrg. Comm. Comput. 11, 157–180]. Our approach differs from the one applied to PBW algebras or G-algebras since our algebras have zero divisors. We use this technique to obtain an algorithm to solve the ideal membership problem.
KeywordsLeibniz algebra, Universal enveloping algebra, Poincaré–Birkhoff–Witt theorem, Gröbner bases
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717108001430
LanguageEnglish
JournalJournal of Symbolic Computation
Volume44
Number5
Pages517 - 526
Year2009
NoteSpanish National Conference on Computer Algebra
Edition0
Translation No
Refereed No
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