S-Space College of Natural Sciences (자연과학대학) Dept. of Mathematical Sciences (수리과학부) Journal Papers (저널논문_수리과학부)
Linear algebraic approach to Grobner-Shirshov basis theory
- Kang, Seok-Jin; Lee, Dong-il; Lee, Kyu-Hwan; Park, Hyungju
- Issue Date
- J. Algebra 313 (2007) 988-1004
- Gröbner–Shirshov basis; Gröbner–Shirshov pair; Monomial basis; Macaulay matrix; Noncommutative algebra; Representation; Simple Lie algebra; Universal enveloping algebra
- 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.
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