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Linear algebraic approach to Grobner-Shirshov basis theory
Cited 14 time in
Web of Science
Cited 14 time in Scopus
- Authors
- Issue Date
- 2007-07-15
- Publisher
- Elsevier
- Citation
- J. Algebra 313 (2007) 988-1004
- Keywords
- Gröbner–Shirshov basis ; Gröbner–Shirshov pair ; Monomial basis ; Macaulay matrix ; Noncommutative algebra ; Representation ; Simple Lie algebra ; Universal 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
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