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Courses and Seminars :: Students and Postgraduates :: Publications
Zolotykh Andrej Alexeevich
Ph.D., Senior researcher, scientific secretary of the PTC laboratory
A.A.Zolotykh was born on September 18th, 1964 in Kursk.
He was graduated from the Moscow State University in 1986. After this he started to work on his dissertation.
His Ph.D. thesis "The Theory of Trace Identities with Involution of Matrix Algebras and Superalgebras" was successfully defended in 1989.
He works in the Moscow State University since 1988.
Area of scientific interests. The theory of trace identities with involution of matrix algebras and superalgebras is developed; an automaton bypassing all labyrinths
with barriers bounded in some directions is constructed; the theory of the differential calculus for
free Lie algebras and superalgebras is obtained; an example of a nonfree Lie algebra of the cohomological dimension one is found;
all projective representations of finite Abelian groups are described;
the classification of all finite gradings of special linear Lie algebras is given.
A.A.Zolotykh has more than 60 published papers. He is the author of a monograph on the combinatorial problems of Lie superalgebras (together with A.A.Mikhalev).
A.A.Zolotykh is a member of the Editorial Board of the Journal "Fundamentalnaya i Prikladnaya Matematika" ("Fundamental and Applied Mathematics").
Email: a dоt zolotykh аt intsys dоt msu dоt ru
Publications of Andrej Alexeevich Zolotykh
Zolotykh A.A. Classification of projective representations of finite Abelian groups.
Vestnik Moskov. Univ. Ser. I Mat. Mekh. 2002, No 3.
Pp. 3-10
Mikhalev A.A.
, Zolotykh A.A. Algorithms of Groebner-Shirshov standard bases construction for ideals of free algebras over commutative rings.
Programmirovanie, 1998, No 6.
Pp. 10-11
Mikhalev A.A.
, Zolotykh A.A. Standard bases for ideals of free algebras over commutative rings.
International Congress of Mathematicians. Abstracts of Short Communications and Poster Sessions. Berlin, 1998.
P. 32
Mikhalev A.A.
, Zolotykh A.A. Standard Groebner-Shirshov bases of free algebras over rings.
Kurosh Algebraic Conference. Abstracts of Talks. Moscow, 1998
P. 87
Mikhalev A.A.
, Zolotykh A.A. Standard Groebner-Shirshov bases of free algebras over rings, I. Free associative algebras.
Internat. J. of Algebra Comput. 8 (1998).
Pp. 689-726
Mikhalev A.A.
, Zolotykh A.A. Standard bases of two-sided ideals of free associative algeras over polynomial rings.
Proc. of the 5th Mathematical Conference of Moscow State Social University. Moscow, 1997.
Pp. 100-104
Zolotykh A.A. Tensor product decomposition and other algorithms for representations of large simple Lie algebras.
Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation. Maui, Hawaii, USA, ACM Press, 1997.
Pp. 60-67
Mikhalev A.A.
, Zolotykh A.A. The complex of algorithms for calculations in Lie superalgebras.
Programmirovanie, 1997, No 1.
Pp. 12-23
Mikhalev A.A., Yu Jie-Tai
, Zolotykh A.A. Images of coordinate polynomials.
Algebra Colloquium, 4:2 (1997).
Pp. 159-162
Zolotykh A.A. Commutation factors and varieties of associative algebras.
Fundamentalnaya i Prikladnaya Matematika 3 (1997), No 2.
Pp. 453-468
Mikhalev A.A.
, Zolotykh A.A. Primitive elements of free Lie algebras.
International Conference on Computational Modelling and Computing in Physics. Book of Abstracts. Dubna, 1996.
P. 105
Mikhalev A.A.
, Zolotykh A.A. A system of algorithms for symbolic calculations in Lie superalgebras.
3rd International Workshop New Computer Technologies in Control Systems. Proceedings of International Workshop. Pereslavl-Zalessky, 1996.
P. 46
Mikhalev A.A.
, Zolotykh A.A. Primitive elements of free algebras.
Ring Theory Conference. Abstracts. Miskolc, 1996.
P. 41
Zolotykh A.A. Varieties of associative algebras generated by e-commutative polynomials.
Ring Theory Conference. Abstracts. Miskolc, 1996.
Pp. 71-72
Mikhalev A.A.
, Zolotykh A.A. Complement algorithms for primitive systems of elements of free Lie algebras with respect to a free generating set.
Intellektual'nye sistemy 1 (1996), No 1-4.
Pp. 173-183
Mikhalev A.A.
, Zolotykh A.A. Algorithms for primitive elements of free Lie algebras and Lie superalgebras.
Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation. Zurich, ACM Press, 1996.
Pp. 161-169
Mikhalev A.A., Shpilrain V.E.
, Zolotykh A.A. Subalgebras of free algebras.
Proc. Amer. Math. Soc. 124 (1996).
Pp. 1977-1984.
Mikhalev A.A.
, Zolotykh A.A. Ranks of subalgebras of free Lie superalgebras.
Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1996, No 2.
Pp. 36-40
Mikhalev A.A., Umirbaev U.U.
, Zolotykh A.A. A Lie algebra with cohomological dimension one over a field of prime characteristic is not necessary free.
Proc. of the Tainan-Moscow Algebra Workshop. Berlin, Walter de Grueter, 1996.
Pp. 37-64
Zolotykh A.A. The equivalence of the irreducible representations of finite dimensional Lie superalgebras with the same identities.
Fundamentalnaya i Prikladnaya Matematika 2 (1996), No 1.
Pp. 289-293
Mikhalev A.A.
, Zolotykh A.A. Test elements for monomorphisms of free Lie algebras and Lie superalgebras.
Comm. Algebra 23 (1995).
Pp. 4995-5001
Mikhalev A.A.
, Zolotykh A.A. An inverse function theorem for free Lie algebras over commutative rings.
Algebra Colloq. 2 (1995), No 3.
Pp. 213-220
Mikhalev A.A.
, Zolotykh A.A. Bases of free super shuffle algebras.
Uspekhi Mat. Nauk 50 (1995), No 1.
Pp. 199-200
Mikhalev A.A.
, Zolotykh A.A. Combinatorial aspects of Lie superalgebras.
CRC Press, Boca Raton, 1995. viii+260 pp.
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Mikhalev A.A.
, Zolotykh A.A. An inverse function theorem for free associative algebras over commutative rings.
Internat. Conf. Semigroups with Applications. Short Communications. S.-Peterburg, 1995.
P. 39
Mikhalev A.A.
, Zolotykh A.A. Natural basis for e-shuffle algebras.
Formal Power Series and Algebraic Combinatorics. 7th Conference. Universite de Marne-la-Vallee, France, 1995.
Pp. 423-426
Mikhalev A.A.
, Zolotykh A.A. Endomorphisms of free associative algebras over commutative rings and their Jacobian matrices.
Fundamentalnaya i Prikladnaya Matematika 1 (1995).
Pp. 177-190
Mikhalev A.A.
, Zolotykh A.A. Applications of Fox differential calculus to free Lie superalgebras.
Non-Associative Algebra and Its Applications. Ed. S.Gonzalez. Kluwer Acad. Publ. Dordrecht, 1994.
Pp. 285-290
Mikhalev A.A.
, Zolotykh A.A. Shuffle superalgebras.
Fundamental Problems of Mathematics and Mechanics. Mathematics. Moscow State University, 1994.
Pp. 279-280
Mikhalev A.A.
, Zolotykh A.A. Rank and primitivity of elements of free colour Lie (p-)superalgebras.
Internat. J. of Algebra and Comput. 4 (1994).
Pp. 617-656
Mikhalev A.A.
, Zolotykh A.A. Endomorphisms of free Lie superalgebras and their Jacobian matrices.
Mathematical Models and Methods in Social Sciences. Proc. of the 2nd Mathematical Conference of Moscow State Social University, Moscow, 1994.
Pp. 58-61
Mikhalev A.A.
, Zolotykh A.A. Automorphisms and primitive elements of free Lie superalgebras.
Comm. Algebra 22 (1994).
Pp. 5889-5901
Mikhalev A.A.
, Zolotykh A.A. Free differential calculus in free Lie superalgebras.
International Congress of Mathematicians. Short Communications. Zurich, 1994.
P. 18.
Mikhalev A.A.
, Zolotykh A.A. Free color shuffle algebras.
Internat. Conf. Algebra and Analysis. Abstracts of Reports. Kazan, 1994, Part I.
P. 138.
Mikhalev A.A.
, Zolotykh A.A. Rank of an element of the free Lie (p-)superalgebra.
Doklady Akad. Nauk 334 (1994), No 6.
Pp. 690-693
Mikhalev A.A., Umirbaev U.U.
, Zolotykh A.A. An example of a nonfree Lie algebra of cohomological dimension one.
Uspekhi Mat. Nauk 49 (1994), No 1.
Pp. 203-204
Mikhalev A.A.
, Zolotykh A.A. The rank of an element of a free color Lie (p-)superalgebra.
Internat. Conf. on Algebra. Abstracts of Reports. Krasnoyarsk, 1993.
P. 418.
Mikhalev A.A.
, Zolotykh A.A. Endomorphism of the free Lie algebra preserving primitivity of elements is an automorphism.
Uspekhi Mat. Nauk 48 (1993), No 6.
Pp. 149-150
Zolotykh A.A. The bypass of labyrinths with barriers bounded in some directions.
Diskret. Mat. 5 (1993), No 1.
Pp. 59-69
Zolotykh A.A. Trace identities of matrix superalgebras with involution.
Contemp. Math. 131.2 (1992).
Pp. 413-432
Zolotykh A.A. A package for computations in simple Lie algebra representations.
IV International Conference on Computer Algebra in Physical Researches. Ed. D.V.Shirkov, V.A.Rostovtsev, V.P.Gerdt. World Scientific, Singapore, 1991.
Pp. 313-316
Zolotykh A.A. Identities of minimal representations of orthogonal Lie algebras.
Abelevy Gruppy i Moduli 10 (1991).
Pp. 31-45
Zolotykh A.A. A package for computations in simple Lie algebra representations.
Proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation. Bonn, ACM Press, 1991.
Pp. 237-238
Zolotykh A.A. An arbitrary ideal of *-identities has a finite base.
Internat. Conf. on Algebra. Abstracts of Reports on Theory of Rings, Algebras and Modules. Barnaul, 1991.
P. 189.
Zolotykh A.A. On ideal of weak identities with extended influence rule.
Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1991, No 4.
Pp. 11-15
Zolotykh A.A., Zyrichev A.N.
Automata which are universal for some classes of labyrinths.
Problems of Theoretical Cybernetics. Abstracts of Reports of 9th All-Union Conference, part I (1). Volgograd, 1990.
P. 48.
Zolotykh A.A. Trace identities of matrix superalgebras with an involution.
Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990), No 4.
Pp. 694-725
Zolotykh A.A. On finiteness of basis of identities of some associative-Lie pairs.
6th Simp. on Theory of Rings, Algebras and Modules. Abstracts of Reports. Lvov, 1990.
P. 60.
Mikhalev A.A.
, Zolotykh A.A. On Witt's superformula and Klyachko's theorem.
6th All-Union Conf. on the Theory of Varieties of Algebraic Systems. Abstracts of Reports. Magnitogorsk, 1990.
P. 16.
Zolotykh A.A. On trace identities of associative-Jordan pairs.
6th All-Union Conf. on the Theory of Varieties of Algebraic Systems. Abstracts of Reports. Magnitogorsk, 1990.
P. 15.
Zolotykh A.A. On calculation of integer-valued characteristics of representations of simple Lie algebras.
4th Internat. Conf. on Computer Algebra in Phys. Researches. Abstracts of Reports. Dubna, 1990.
P. 75.
Zolotykh A.A. On identities of representations of Lie superalgebras.
4th All-Union Conf. Lie Algebras and Their Applications in Mathematics and Physics. Abstracts of Reports. Kazan, 1990.
P. 22.
Zolotykh A.A. The Theory of Trace Identities with Involution of Matrix Algebras and Superalgebras.
Ph. D. Thesis. Moscow State Univ., 1989.
125 pp.
Zolotykh A.A. The Theory of Trace Identities with Involution of Matrix Algebras and Superalgebras.
Ph. D. Thesis Summary. Moscow State Univ., 1989.
16 pp.
Zolotykh A.A. Trace identities with involution of matrix superalgebras.
Internat. Conf. on Algebra. Abstracts of Reports in the Theory of Rings, Algebras and Modules. Novosibirsk, 1989.
P. 55.
Zolotykh A.A. On Multiplicative Characters, Constructed with the Use of the Full Matrix Algebras with Involution.
Moscow, 1989. Deposited at VINITI, No 2840-89.
51 pp.
Zolotykh A.A. Decomposition of Tensor Products of Representations of Lie Algebra E8.
Moscow, 1988. Deposited at VINITI, No 8360-88.
130 pp.
Zolotykh A.A. Multiplicative characters of the minimal representations of orthogonal and symplectic Lie algebras.
5th Siberian Conf. on Varieties of Algebraic Systems. Abstracts of Reports. Barnaul, 1988.
Pp. 26-30
Sukhanov A.A.
, Zolotykh A.A. Algorithms of calculation of integer-valued characteristics of classical Lie algebras and Lie groups.
Calculating Invariants in the Theory of Algebraic Systems. Collection of Scientific Papers. Novosibirsk, 1987.
Pp. 67-79
Zolotykh A.A. On 4-Engel Lie algebras.
Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1986, No 2.
Pp. 79-81
Razmyslov Yu. P.
, Zolotykh A.A. On 4-Engel Lie algebras.
9th All-Union Simp. on Group Theory. Abstracts of Reports. Moscow, 1984.
Pp. 201-202
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