Serre relations and Gröbner-Shirshov bases for simple lie algebras I

International Journal of Algebra and Computation

Volumn 6, Issue 4, 1996, Pages 389-400

  Bokut, L A ^a   Klein, A A ^b  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030499976     PISSN: 02181967     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218196796000222     Document Type: Article

References (20)

1. S. Berman, On the construction of simple Lie algebras, J. of Algebra 27 (1973) 158-183.
2. L. A. Bokut, Imbedding of Lie algebras into algebraically closed Lie algebras, Algebra and Logic 1 (1962) 47-53.
3. L. A. Bokut, Unsolvability of the equality problem and subalgebras of finitely presented Lie algebras, Math. USSR Izvestia 6 (1972) 1153-1199.
4. L. A. Bokut, On algebraically closed and simple Lie algebras, Trudy Steklov Math. 148 (1978) 30-42; Proc. Steklov Inst. Math. 4 (1980) 27-39.
5. L. A. Bokut, On algebraically closed and simple Lie algebras, Trudy Steklov Math. 148 (1978) 30-42; Proc. Steklov Inst. Math. 4 (1980) 27-39.
6. L. A. Bokut and G. P. Kukin, Algorithmic and combinatorial algebra, Kluwer, Dordrecht 1994.
7. K. T. Chen, R. H. Fox and R. C. Lyndon, Free differential calculus IV, The quotient groups of the lower central series, Ann. Math. 68 (1958) 81-95.
8. P. M. Cohn, Universal algebra, Harper and Row, New York 1965.
9. M. Hall, A basis for free Lie rings and higher commutators in free groups, Proc. Amer. Math. Soc. 1 (1950) 575-581.
10. J. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, 40 Springer-Verlag, New York 1972.
11. N. Jacobson, Lie algebras, Wiley, New York 1962.
12. P. Lalonde and A. Ram, Standard Lyndon bases of Lie algebras and enveloping algebras, Trans. Amer. Math. Soc. 347 (1995) 1821-1830.
13. M. Lothaire, Combinatorics on words, Encycl. Math. 17, Addison Wesley, Reading, Mass. 1983.
14. G. B. Seligman, Modular Lie algebras, Springer-Verlag, New York 1967.
15. J. P. Serre, Complex semisimple Lie algebras, Springer-Verlag, New York 1987.
16. A. I. Shirshov, On free Lie rings, Math. Sb. 45 87 (1958) 113-122.
17. A. I. Shirshov, On bases of free Lie algebras, Algebra and Logic 1 (1962) 14-19.
18. A. I. Shirshov, Some algorithmic problems for Lie algebras, Sib. Math. J. 3 (1962) 292-296.
19. A. I. Shirshov, On one hypothesis of the theory of Lie algebras, Sib. Math. J. 3 (1962) 297-301.
20. V. A. Ufnarovski, Combinatorial and asymptotic methods in algebra, Algebra 6, VINITI, Moscow 1990, 5-177.