Constructing bases of finitely presented Lie algebras using Gröbner bases in free algebras

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Constructing bases of finitely presented Lie algebras using Gröbner bases in free algebras

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1999 international symposium on Symbolic and algebraic computation table of contents

Vancouver, British Columbia, Canada

Pages: 37 - 43

Year of Publication: 1999

ISBN:1-58113-073-2

Authors

W. A. de Graaf	School of Mathematical and Computational Sciences, University of St. Andrews, St. Andrews Scotland
J. Wisliceny	Schwaaner Str. 45, 18273 Güstrow, Germany

Sponsors

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
SIGNUM: ACM Special Interest Group on Numerical Mathematics

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ACM New York, NY, USA

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Downloads (6 Weeks): 6, Downloads (12 Months): 16, Citation Count: 1

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	BAHTURIN, Y. A., MIKHALEV, A. A., PETROGRAD- SKY, V. M., AND ZAIC, EV, M. V. Infinite-dimensional Lie superalgebras. XYalter de Gruyter & Co., Berlin, 1992.
	2	BERGMA.N.G.M. The diarnond lcmma for ring theory. Adv. in Math. 29, 2 (1978), 178-218.
	3	BOURBAKI, N. Groupes et Alg~bres de. Lie, Chapitre II. Hermann, Paris, 1972.
	4	COHEN, A. M.. STEINBACH. A.. USHIROBIRA, a., AND WAI,ES, D. Lie algebr~ generated by extremal elements, preliminary version, December 1998.
	5	THE GAP GROUP. GAP- Groups, Algorithms, and Programming, Version ~,. Aachen, St Andrews, 1998. (http'//www-gap. dcs. st-and, ac. uk/-gap).
	6	Vladimir P. Gerdt , Vladimir V. Kornyak, Construction of finitely presented Lie algebras and superalgebras, Journal of Symbolic Computation, v.21 n.3, p.337-349, March 1996 [doi>10.1006/jsco.1996.0016]
	7	George Havas , M. F. Newman , M. R. Vaughan-Lee, A nilpotent quotient algorithm for graded Lie rings, Journal of Symbolic Computation, v.9 n.5-6, p.653-664, May/June 1990 [doi>10.1016/S0747-7171(08)80080-6]
	8	LALONDE. P., ANI) RAM, A. Standaxd Lyndon bases of Lie algebras and enveloping algebras. Trans. Amer. Math. Soc. ,'}dT, 5 (1995), 1821-1830.
	9	LINTON, S. A. On vector enumeration. Linear Algebra and its Applications 192 (1993), 235-248. Computational linear algebra in algebraic and related problems (Esse11, 1992).
	10	Teo Mora, An introduction to commutative and noncommutative Gro¨bner bases, Selected papers of the second international colloquium on Words, languages and combinatorics, p.131-173, November 1994, Kyoto, Japan
	11	SERRE, J.-P. Alg~bres de Lie semi-simples complexes. W. A. Benjamin, inc., New York-Amsterdam, 1966.
	12	SHIRSHOV, A. I. Some algorithmic problems for Lie algebras. Sib. Mat. Zh. 3 (1962), 292-296. (Russian).
	13	UFNAR.OVSKIJ, V. A. Combinatorial and Asymptotic Methods in Algebra, vol. 57 of Encyclopedia of Mathematical Sciences. Springer Verlag, Berlin, Heidelberg, New York, 1995, oh. I, pp. 1-196.
	14	VAN LEEUWEN, M. i. A., AND ROELOFS, M. Termination for a class of algorithms for constructing algebras given by generators and relations. Journal of Pure and Applied Algebra 117//118 (1997), 431-445. Algorithms for algebra (Eindhoven, 1996).
	15	Michael Vaughan-Lee, An algorithm for computing graded algebras, Journal of Symbolic Computation, v.16 n.4, p.345-354, Oct. 1993 [doi>10.1006/jsco.1993.1052]
	16	VAUGHAN-LEE, M. a. Oil Zel'manov's solution of the restricted Burnside problem. J. Group Theory 1, 1 (1998), 65-94.

CITED BY 2

	Serena Cicalò , Willem de Graaf, Non-associative gröbner bases, finitely-presented lie rings and the engel condition, Proceedings of the 2007 international symposium on Symbolic and algebraic computation, July 29-August 01, 2007, Waterloo, Ontario, Canada
	Serena Cicalò , Willem A. de Graaf, Non-associative Gröbner bases, finitely-presented Lie rings and the Engel condition, II, Journal of Symbolic Computation, v.44 n.7, p.786-800, July, 2009