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TitlePoincaré–Birkhoff–Witt theorem for Leibniz -algebras
Author(s) José Manuel Casas, Manuel A. Insua, Manuel Ladra
TypeArticle in Journal
AbstractWe construct the universal enveloping algebra of a Leibniz n -algebra and we prove that the category of modules over this algebra is equivalent to the category of representations. We also give a proof of the Poincaré–Birkhoff–Witt theorem for universal enveloping algebras of finite-dimensional Leibniz n -algebras using Gröbner bases in a free associative algebra.
KeywordsLeibniz n -algebra, Universal enveloping algebra, Poincaré–Birkhoff–Witt theorem, Gröbner bases
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717107000995
LanguageEnglish
JournalJournal of Symbolic Computation
Volume42
Number11–12
Pages1052 - 1065
Year2007
NoteNon-commutative Gröbner bases and applications
Edition0
Translation No
Refereed No
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