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TitleGrobner-Shirshov Bases for Dialgebras
Author(s) Leonid A. Bokut, yugon Chen, Cihua Liu
TypeArticle in Journal
AbstractIn this paper, we define the Gröbner–Shirshov basis for a dialgebra. The Composition–Diamond lemma for dialgebras is given then. As a result, we give Gröbner–Shirshov bases for the universal enveloping algebra of a Leibniz algebra, the bar extension of a dialgebra, the free product of two dialgebras, and Clifford dialgebra. We obtain some normal forms for algebras mentioned the above.
KeywordsDialgebra; Gröbner–Shirshov basis; Leibniz algebra; Clifford dialgebra
URL DOI: 10.1142/S0218196710005753
LanguageEnglish
JournalInternational Journal of Algebra and Computation (IJAC)
Volume20
Number3
Pages391-415
Year2010
Translation No
Refereed Yes
SponsorsSupported by the NNSF of China (Nos. 10771077, 10911120389) and the NSF of Guangdong Province (No. 06025062)
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