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Linear algebraic approach to Grobner-Shirshov basis theory

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dc.contributor.authorKang, Seok-Jin-
dc.contributor.authorLee, Dong-il-
dc.contributor.authorLee, Kyu-Hwan-
dc.contributor.authorPark, Hyungju-
dc.date.accessioned2009-11-16-
dc.date.available2009-11-16-
dc.date.issued2007-07-15-
dc.identifier.citationJ. Algebra 313 (2007) 988-1004en
dc.identifier.issn0021-8693-
dc.identifier.urihttp://hdl.handle.net/10371/12163-
dc.description.abstractWe construct a new efficient algorithm for finding Gröbner–Shirshov bases for noncommutative algebras and their representations. This algorithm uses the Macaulay matrix [F.S. Macaulay, On some formula in elimination, Proc. London Math. Soc. 33 (1) (1902) 3–27], and can be viewed as a representation theoretic analogue of the F_4 algorithm developed by J.C. Faugère. We work out some examples of universal enveloping algebras of Lie algebras and of their representations to illustrate the algorithm.en
dc.description.sponsorshipThis research was supported by KRF Grant #2005-070-C00004.en
dc.language.isoen-
dc.publisherElsevieren
dc.subjectGröbner–Shirshov basisen
dc.subjectGröbner–Shirshov pairen
dc.subjectMonomial basisen
dc.subjectMacaulay matrixen
dc.subjectNoncommutative algebraen
dc.subjectRepresentationen
dc.subjectSimple Lie algebraen
dc.subjectUniversal enveloping algebraen
dc.titleLinear algebraic approach to Grobner-Shirshov basis theoryen
dc.typeArticleen
dc.contributor.AlternativeAuthor강석진-
dc.contributor.AlternativeAuthor이동일-
dc.contributor.AlternativeAuthor이규환-
dc.contributor.AlternativeAuthor박형주-
dc.identifier.doi10.1016/j.jalgebra.2007.02.001-
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)
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