Algorithms for primitive elements of free Lie algebras and Lie superalgebras

Subscribe (Full Service)


	Search: The ACM Digital Library The Guide

	Feedback

Algorithms for primitive elements of free Lie algebras and Lie superalgebras

Full text

Pdf (798 KB)

Source

International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1996 international symposium on Symbolic and algebraic computation table of contents

Zurich, Switzerland

Pages: 161 - 169

Year of Publication: 1996

ISBN:0-89791-796-0

Authors

Alexander A. Mikhalev	Department of Mechanics and Mathematics, Moscow State University, Moscow, 119899, Russia
Andrej A. Zolotykh	Department of Mechanics and Mathematics, Moscow State University, Moscow, 119899, Russia

Sponsors

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

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 2, Downloads (12 Months): 15, Citation Count: 0

Additional Information:

references index terms collaborative colleagues peer to peer

Tools and Actions:	Request Permissions Review this Article Save this Article to a Binder Display Formats: BibTeX EndNote ACM Ref

DOI Bookmark:	Use this link to bookmark this Article: http://doi.acm.org/10.1145/236869.236929 What is a DOI?

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	Yu. A. Bahturin, A. A. Mikhalev, M. V. Zaicev, and V. M. Petrogradsky, Infinite Dimensional Lie Superalgebras. Walter de Gruyter Publ., Berlin, New York, 1992.
	2	J. S. Birman, An inverse function theorem for free groups. Proc. Amer. Math. Soc. 41 (1973), 634-638.
	3	L. A. Bokut' and G. P. Kukin, Algorithmic and Combinatorial Algebra. Kluwer Academic Publ., Dordrecht, 1994.
	4	P. M. Cohn, Free Rings and Thew Relations. 2nd Ed. Academic Press, London, New York, 1985.
	5	W. Dicks and J. Lewin, A Jacobian con3ecture for free associative algebras. Comm. Algebra 10 (1982), 1285-1306.
	6	R. H. Fox, Free differential calculus. L Derivations in free group rings. Ann. of Math. (2) 57 (1953), 547-560.
	7	O. G. Kharlampovich and M. V. Sapir, Algorithmic problems in vameties. Internat. J. Algebra Comput. 5 (1995), no 5.
	8	G. P. Kukin, Primitive elements of free Lze algebras. Algebra i Logika 9 (1970), no. 4, 458-472.
	9	R. C. Lyndon and P. E. Shupp, Combinatorial Group Theory. Springer-Verlag, Berlin, 1977.
	10	W. Magnus, A. Kaxrass, and D. Solitar, Combinatorial Group Theory. 2nd Ed. Dover, NY, 1976.
	11	A. A. Mikhalev, Subalgebras of free color L~e superalgebras. Mat. Zametki 37 (1985), no. 5, 653-661. English translation: Math. Notes 37 (1985), 356-360.
	12	A. A. Mikhalev, Free color Lie superalgebras. Dok-- 1. Akad. Nauk 286 (1986), no. 3, 551-554. English translation: Soviet Math. Dokl. 33 (1986), 136-139.
	13	A. A. Mikhalev, Subalgebras of free Lie p-superalge.. bras. Mat. Zametki 43 (1988), no. 2, 178-191. En-. glish translation: Math. Notes 43 (1988), 99-106.
	14	A. A. Mikhalev, The junction lemma and the equality problem for color Lie superalgebras. Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1989, no. 5, 88-91. English translation: Moscow Univ. Math. Bull. 44 (1989), 87-70.
	15	A. A. Mikhalev, On right ideals of the free associative algebra generated by free color Lie (p-)superalgebras. Uspekhi Mat. Nauk 47 (1992), no. 5, 187-188. English translation: Russian Math. Surveys 47 (1992), no. 5, 196-197.
	16	A. A. Mikhalev, The composition lemma for color Lie superalgebras and for Lie p-superalgebras. Contemp. Math. 131.2 (1992), 91-104.
	17	A. A. Mikhalev, Combinatorial theory of Lie superalgebras, iII Int. Conf. on non associative algebra. Oviedo, Spain, 1993. Abstracts of reports, 15-16.
	18	A. A. Mikhalev, Differential Lie superalgebras. Uspekhi Mat. Nauk 48 (1993), no. 5, 179-180. English translation: Russian Math. Surveys 48 (1993), no. 5, 179-180.
	19	A. A. Mikhalev, Shirshov's composition techniques in Lie superalgebras (non-commutative Grb'bner bases). Trudy Sem. Petrovsk. 18 (1995), 277-289.
	20	A. A. Mikhalev, Combinatomal aspects of the theory of Lie superalgebras. Proc. of Tainan-Moscow Algebra Workshop. Walter de Gruyter Publ., Berlin~ 1996, 37-64.
	21	A. A. Mikhalev, V. E. Shpilrain, and A. A. Zolotykh, Subalgebras of free algebras. Proc. Amer. Math. Soc., in press.
	22	A. A. Mikhalev, U. U. Umirbaev, and A. A. Zolotykh, An example of a non/tee Lie algebra of cohomological dimenswn one. Uspekhi Mat. Nauk 49 (1994), no. 1, 203-204. English translation: Russian Math. Surveys 49 (1994), no. 1, p. 254.
	23	A. A. Mikhalev, U. U. Umirbaev, and A. A. Zolotykh, A Lie algebra with cohomologicaI dzmension one over a field of prime charactemstic ~s not necessary free. Proc. of Tainan-Moscow Algebra Workshop. Walter de Gruyter Publ., Berlin, 1996, 241-248.
	24	A. A. Mikhalev and A. A. Zolotykh, Endomorphism of the free L~e algebra preserving primitivity of elements is an automorphism. Uspekhi Mat. Nauk 48 (1993), no. 6, 149-150. English translation: Russian Math. Surveys 48 (1993), no. 6, 189-190.
	25	A. A. Mikhalev and A. A. Zolotykh, Free differential calculus in free Lie superalgebras. Internat. Congress of Math. Short Communications. Zfirich, 1994, p. 18.
	26	A. A. Mikhalev and A. A. Zolotykh, Rank of an element of the free Lie (p-)superalgebra. Dokl. Akad. Nauk 334 (1994), no. 6, 690-693. English translation: Russian Acad. Sci. Dokl. Math. 49 (1994), no. 1, 189-193.
	27	A. A. Mikhalev and A. A. Zolotykh, Applications of Fox differential calculus to free Lie superalgebras. Non-Associative Algebra and its Applications. Kluwer Academic Publ., Dordrecht, 1994, 285-290.
	28	A. A. Mikhalev and A. A. Zolotykh, Rank and primitivity of elements of free color Lie (p-)superalgebras. Internat. J. Algebra Comput. 4 (1994), 617-656.
	29	A. A. Mikhalev and A. A. Zolotykh, Automorphisms and primitive elements of free Lie superalgebras. Comm. Algebra 22 (1994), 5889-5901.
	30	A. A. Mikhalev and A. A. Zolotykh, Combinatorial Aspects of Lie Superalgebras. CRC Press, Boca Raton, New York, 1995.
	31	A. A. Mikhalev and A. A. Zolotykh, An ~nverse function theorem for free Lie algebras over commutative rings. Algebra Colloq. 2 (1995), no. 3, 213-220.
	32	A. A. Mikhalev and A. A. Zolotykh, Endomorphisms of free associative algebras over commutative rings and their Jacobian matrices. Fundamental'naya i Prikladnaya Matematika 1 (1995), 177-190.
	33	A. A. Mikhalev and A. A. Zolotykh, Test elements for monomorphisms of free Lie algebras and superalgebras. Comm. Algebra 23 (1995), 4995-5001.
	34	A. A. Mikhalev and A. A. Zolotykh, Ranks of subalgebras of free Lie superalgebras. Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1996, no. 2, 36-40.
	35	J. Nielsen, Die Isomorphismen der allgemeinen unendlichen Gruppe mit zwei Erzeugenden, Math. Ann. 78 (1918), 385-397.
	36	C. Reutenauer, Applications of a noncommutatwe Jacobian matrix. J. Pure Appl. Algebra 77 (1992), 169-181.
	37	A-. H. Schofield, Representations of Rings over Skew Fields. London Math. Soc. Lecture Note Ser. 92 (~9s5).
	38	V. Shpilrain, On generators of L/R2 Lie algebras. Proc. Amer. Math. Soc. 119 (1993), 1039-1043.
	39	A. S. Shtern, Free Lie superalgebras. Sibirsk. Mat. Zh. 27 (1986), 170-174.
	40	J. R. Stallings, On torsion.free groups with infinitely many ends. Ann. of Math. (2) 88 (1968), no. 2, 312-334.
	41	R. G. Swan, Groups of cohomological d~menswn one. J. Algebra 12 (1969), 585-610.
	42	I. M. Topping, Free generators and the free differential calculus. Thesis. State Univ. New York, Stony Brook, 1973.
	43	U. U. Umirbaev, On Jacobian matmces of Lie algebras. 6th All-Union Conf. on the Varieties of Algebraic Systems. Abstracts of Reports. Magnitogorsk, 1990, 32-33.
	44	U. U. Umirbaev, Partial derivatives and endomorphisms of some relatwely free Lie algebras. Sibirsk. Mat. Zh. 34 (1993), no. 6, 179-188.
	45	U. U. Umirbaev, Some algorithmic questions of associative algebras. Algebra i Logika 32 (1993), no. 4, 45O-47O.
	46	U. U. Umirbaev, Primitive elements of free groups. Uspekhi Mat. Nauk 49 (1994), no. 2, 175-176.
	47	U. U. Umirbaev, A note on primitive elements o/free groups. Proc. of 5th Siberian School "Algebra and Analysis", in press.
	48	J. H. C. Whitehead, On certain sets of elements in a free group. Proc. London Math. Soc. 41 (1936), 48-56.
	49	J.H.C. Whitehead, On equivalent sets of elements in a free group. Ann. of Math. (2) 37 (1936), 782-800.
	50	A. V. Yagzhev, On the algorithmic problem of recognizing automorphisms among endomorphisms of free associative algebras of finite rank. Sibirsk. Mat. Zh. 21 (1980), no. 1, 193-199.