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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 dīt zolotykh ąt intsys dīt msu dīt 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. 310
Mikhalev A.A.
, Zolotykh A.A. Algorithms of GroebnerShirshov standard bases construction for ideals of free algebras over commutative rings.
Programmirovanie, 1998, No 6.
Pp. 1011
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 GroebnerShirshov bases of free algebras over rings.
Kurosh Algebraic Conference. Abstracts of Talks. Moscow, 1998
P. 87
Mikhalev A.A.
, Zolotykh A.A. Standard GroebnerShirshov bases of free algebras over rings, I. Free associative algebras.
Internat. J. of Algebra Comput. 8 (1998).
Pp. 689726
Mikhalev A.A.
, Zolotykh A.A. Standard bases of twosided ideals of free associative algeras over polynomial rings.
Proc. of the 5th Mathematical Conference of Moscow State Social University. Moscow, 1997.
Pp. 100104
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. 6067
Mikhalev A.A.
, Zolotykh A.A. The complex of algorithms for calculations in Lie superalgebras.
Programmirovanie, 1997, No 1.
Pp. 1223
Mikhalev A.A., Yu JieTai
, Zolotykh A.A. Images of coordinate polynomials.
Algebra Colloquium, 4:2 (1997).
Pp. 159162
Zolotykh A.A. Commutation factors and varieties of associative algebras.
Fundamentalnaya i Prikladnaya Matematika 3 (1997), No 2.
Pp. 453468
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. PereslavlZalessky, 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 ecommutative polynomials.
Ring Theory Conference. Abstracts. Miskolc, 1996.
Pp. 7172
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 14.
Pp. 173183
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. 161169
Mikhalev A.A., Shpilrain V.E.
, Zolotykh A.A. Subalgebras of free algebras.
Proc. Amer. Math. Soc. 124 (1996).
Pp. 19771984.
Mikhalev A.A.
, Zolotykh A.A. Ranks of subalgebras of free Lie superalgebras.
Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1996, No 2.
Pp. 3640
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 TainanMoscow Algebra Workshop. Berlin, Walter de Grueter, 1996.
Pp. 3764
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. 289293
Mikhalev A.A.
, Zolotykh A.A. Test elements for monomorphisms of free Lie algebras and Lie superalgebras.
Comm. Algebra 23 (1995).
Pp. 49955001
Mikhalev A.A.
, Zolotykh A.A. An inverse function theorem for free Lie algebras over commutative rings.
Algebra Colloq. 2 (1995), No 3.
Pp. 213220
Mikhalev A.A.
, Zolotykh A.A. Bases of free super shuffle algebras.
Uspekhi Mat. Nauk 50 (1995), No 1.
Pp. 199200
Mikhalev A.A.
, Zolotykh A.A. Combinatorial aspects of Lie superalgebras.
CRC Press, Boca Raton, 1995. viii+260 pp.

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 eshuffle algebras.
Formal Power Series and Algebraic Combinatorics. 7th Conference. Universite de MarnelaVallee, France, 1995.
Pp. 423426
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. 177190
Mikhalev A.A.
, Zolotykh A.A. Applications of Fox differential calculus to free Lie superalgebras.
NonAssociative Algebra and Its Applications. Ed. S.Gonzalez. Kluwer Acad. Publ. Dordrecht, 1994.
Pp. 285290
Mikhalev A.A.
, Zolotykh A.A. Shuffle superalgebras.
Fundamental Problems of Mathematics and Mechanics. Mathematics. Moscow State University, 1994.
Pp. 279280
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. 617656
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. 5861
Mikhalev A.A.
, Zolotykh A.A. Automorphisms and primitive elements of free Lie superalgebras.
Comm. Algebra 22 (1994).
Pp. 58895901
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. 690693
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. 203204
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. 149150
Zolotykh A.A. The bypass of labyrinths with barriers bounded in some directions.
Diskret. Mat. 5 (1993), No 1.
Pp. 5969
Zolotykh A.A. Trace identities of matrix superalgebras with involution.
Contemp. Math. 131.2 (1992).
Pp. 413432
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. 313316
Zolotykh A.A. Identities of minimal representations of orthogonal Lie algebras.
Abelevy Gruppy i Moduli 10 (1991).
Pp. 3145
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. 237238
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. 1115
Zolotykh A.A., Zyrichev A.N.
Automata which are universal for some classes of labyrinths.
Problems of Theoretical Cybernetics. Abstracts of Reports of 9th AllUnion 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. 694725
Zolotykh A.A. On finiteness of basis of identities of some associativeLie 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 AllUnion Conf. on the Theory of Varieties of Algebraic Systems. Abstracts of Reports. Magnitogorsk, 1990.
P. 16.
Zolotykh A.A. On trace identities of associativeJordan pairs.
6th AllUnion Conf. on the Theory of Varieties of Algebraic Systems. Abstracts of Reports. Magnitogorsk, 1990.
P. 15.
Zolotykh A.A. On calculation of integervalued 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 AllUnion 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 284089.
51 pp.
Zolotykh A.A. Decomposition of Tensor Products of Representations of Lie Algebra E_{8}.
Moscow, 1988. Deposited at VINITI, No 836088.
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. 2630
Sukhanov A.A.
, Zolotykh A.A. Algorithms of calculation of integervalued characteristics of classical Lie algebras and Lie groups.
Calculating Invariants in the Theory of Algebraic Systems. Collection of Scientific Papers. Novosibirsk, 1987.
Pp. 6779
Zolotykh A.A. On 4Engel Lie algebras.
Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1986, No 2.
Pp. 7981
Razmyslov Yu. P.
, Zolotykh A.A. On 4Engel Lie algebras.
9th AllUnion Simp. on Group Theory. Abstracts of Reports. Moscow, 1984.
Pp. 201202
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