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Linear algebraic approach to Grobner-Shirshov basis theory

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Authors
Kang, Seok-Jin; Lee, Dong-il; Lee, Kyu-Hwan; Park, Hyungju
Issue Date
2007-07-15
Publisher
Elsevier
Citation
J. Algebra 313 (2007) 988-1004
Keywords
Gröbner–Shirshov basisGröbner–Shirshov pairMonomial basisMacaulay matrixNoncommutative algebraRepresentationSimple Lie algebraUniversal enveloping algebra
Abstract
We 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.
ISSN
0021-8693
Language
English
URI
http://hdl.handle.net/10371/12163
DOI
https://doi.org/10.1016/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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