Dimitry Leites - Theses supervised

PhD

1979

A. Shapovalov, Irreducible representations of finite-dimensional Hamiltonian and Poisson Lie superalgebras, Moscow State University (co-advisor: A.I. Kostrikin).

Finite-dimensional irreducible representations of Hamiltonian Lie superalgebras, Mat. Sbornik 107 (1978), 259-274 (in Russian). English translation: Math. USSR-Sbornik 35 (1979), 541-554. MR 80h:17016
Invariant differential operators and irreducible representations of finite-dimensional Hamiltonian and Poisson Lie superalgebras, Serdica Bulgar. Math. Publ. 7 (1981), 337-342 (in Russian). MR 83i:17015b

1983

G. Shmelev, Irreducible representations of infinite-dimensional Hamiltonian and Poisson Lie superalgebras, Moscow State University (co-advisor: A.A. Kirillov).

Irreducible representations of infinite-dimensional Hamiltonian and Poisson Lie superalgebras, and invariant differential operators, Serdica Bulg. Math. Publ. 8 (1982), no.4, 408-417 (in Russian). MR 84k:58088a
Irreducible representations of Poisson Lie superalgebras, and invariant differential operators, Funkts. Anal. Prilozh. 17 (1983), no.1, 91-92 (in Russian); English translation: Funct. Anal. Appl. 17 (1983), no.1, 76-77. MR 84k:58088b
\(H(2n,m)\)-invariant differential operators and irreducible \(osp(2,2n)\)-representations, Funkts. Anal. Prilozh. 17 (1983), no.4, 94-95 (in Russian); English translation: Funct. Anal. Appl. 17 (1983), 323-325. MR 85a:17012
Invariant operators on a symplectic supermanifold, Mat. Sbornik 120 (1983), no.4, 528-539 (in Russian); English translation: Math. USSR-Sbornik 48 (1984), no.2, 521-533. MR 84j:17007

P. Grozman, Invariant differential operators, Moscow State University (co-advisor: V. Palamodov).

Classification of bilinear invariants of operators on tensor fields, Funkts. Anal. Prilozh. 14 (1980), no.2, 58-59; English translation: Funct. Anal. Appl. 14 (1980), no.2, 127-128. MR 82b:58008
[G] On bilinear invariant differential operators acting on tensor fields on the symplectic manifold, J. Nonlin. Math. Phys. 8 (2001), no.1, 31-37; arXiv:math/0101266. MR 2003a:53111
Invariant bilinear differential operators, arXiv:math/0509562.

A. Sergeev, Invariant polynomials on Lie superalgebras, Moscow State University (co-advisor: A.A. Kirillov).

[S1] The invariant polynomials on simple Lie superalgebras, Represent. Theory. 3 (1999), 250-280; arXiv:math/9810111. MR 2000k:17012
[S2] An analog of the classical invariant theory for Lie superalgebras. I, II, Michigan Math. J. 49 (2001), no.1, 113-146, 147-168; arXiv:math/9810113, arXiv:math/9904079. MR 2003d:17008
A.N. Sergeev and A.P. Veselov, Grothendieck rings of basic classical Lie superalgebras, Ann. Math. 173 (2011), no.2, 663-703; arXiv:0704.2250. MR 2012a:17011

1986

Yu. Kochetkov, Differential operators invariant with respect to Lie superalgebras preserving odd canonical form, Leningrad State University (co-advisor: A.L. Onishchik).

1987

A. Vaintrob, Deformations of complex structures on supermanifolds, Moscow State University (co-advisor: Yu. Manin).

Published in:

Deformation of complex superspaces and of the coherent sheaves on them, Itogi Nauki i Tekhniki. Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Vol. 32, 1988, VINITI, Moscow, 125-211 (in Russian); English translation: J. Soviet Math. 51 (1990), no.1, 2140-2188. MR 90h:32049

1988

V. Serganova, Automorphisms and real forms of simple Lie superalgebras, Leningrad State University (co-advisor: A.L. Onishchik).

For full details, see Appendix to [E7].

V. Shander, Vector fields and differential equations on supermanifolds, Voronezh State University, Russia (co-advisor: S. Gindikin).

Complete integrability of ordinary differential equations on supermanifolds, Funkts. Anal. Prilozh. 17 (1983), no.1, 89-90 (in Russian); English translation: Funct. Anal. Appl. 17 (1983), no.1, 74-75. MR 84g:58058
For details, see [B3].

1990

G. Vinel, Symmetric superdomains and Lie triple systems, University of Connecticut (co-advisor: W. Abikoff).

A. Elduque, New simple Lie superalgebras in characteristic 3, J. Algebra 296 (2006), no.1, 196-233; arXiv:math/0412395. MR 2006i:17028

1991

A. Stolin, On rational solutions of the classical Yang-Baxter equation, Stockholm University (co-advisor: V. Drinfeld).

On rational solutions of Yang-Baxter equation for \(\mathfrak{sl}(n)\), Math. Scand. 69 (1991), 57-80. MR 93d:17023
Constant solutions of Yang-Baxter equation for \(\mathfrak{sl}(2)\) and \(\mathfrak{sl}(3)\), Math. Scand. 69 (1991), 81-88. MR 93b:17053
On rational solutions of Yang-Baxter equations. Maximal orders in loop algebra, Comm. Math. Phys. 141 (1991), no.3, 533-548. MR 93b:17052

1992

E. Poletaeva, The local structure of classical superdomains, Penn State (co-advisors: J.L. Brylinsky, A.L. Onishchik).

For full details, see SoS preprint 36/2003.

2002

I. Bider, State-oriented business process modeling - principles, theory and practice, Royal Institute of Technology, Stockholm (co-advisor: P. Johannesson).

2008

A. Lebedev, Simple modular Lie superalgebras, Leipzig University.

Analogs of the orthogonal, Hamiltonian, Poisson, and contact Lie superalgebras in characteristic \(2\), J. Nonlin. Math. Phys. 17 (2010), Special issue in memory of F. Berezin, 217-251. MR 2827481

2010

P. Zusmanovich, Low-dimensional cohomology of current Lie algebras, Stockholm Univerity (co-advisor: R. Bøgvad).

Master's

1977

A. Shapovalov, Irreducible representations of Hamiltonian Lie superalgebra, Moscow State University.

1978

S. Eliseev, Irreducible representations of Lie superalgebra \(q(2)\), Moscow State University.

V. Shander, Normal forms of vector fields on supermanifolds, Moscow State University.

Vector fields and differential equations on supermanifolds, Funkts. Anal. Prilozh. 14 (1980), no.2, 91-92 (in Russian); English translation: Funct. Anal. Appl. 14 (1980), no.2, 160-162. MR 82c:58004
Lie algebroids and homological vector fields, Uspekhi Mat. Nauk 52 (1997), no.2, 161-162 (in Russian); English translation: Russ. Math. Surv. 52 (1997), no.2, 428-429. MR 1480150

P. Grozman, Invariant differential operators, Moscow State University.

E. Korkina, Gelfand-Tsetlin basis for irreducible representations of \(gl(2|2)\), Moscow State University.

1979

A. Vaintrob, New invariant differential operators, Moscow State University.

Published in [44].

A. Kutin, Noncommutativity of the superalgebra of complex numbers and consequences, Moscow State University.

1980

G. Shmelev, Irreducible representations of infinite-dimensional Hamiltonian Lie superalgebra, Moscow State University

A. Sergeev, Invariant polynomials on Lie superalgebras, Moscow State University.

1981

V. Serganova, Automorphisms and real forms of finite-dimensional Lie superalgebras, Moscow State University.

E. Poletaeva, Affine actions of stringy superalgebras, Moscow State University.

Cited in [91].

1983

L. Tsalenko, Witt's formula for free Lie superalgebra, Moscow State University.

A.I. Molev and L.M. Tsalenko, Representations of the symmetric group in the free Lie (super-)algebra and in the space of harmonic polynomials, Funkts. Anal. Prilozh. 20 (1986), no.2, 76-77 (in Russian); English translation: Funct. Anal. Appl. 20 (1986), no.2, 150-152. MR 87k:17006
S.-J. Kang and J.-H. Kwon, Graded Lie superalgebras, supertrace formula, and orbit Lie superalgebras, Proc. London Math. Soc. 81 (2000), 675-724; arXiv:math/9809025. MR 2001f:17057
V. Petrogradsky, Witt's formula for restricted Lie algebras, Adv. Appl. Math. 30 (2003), no.1-2, 219-227. MR 2004c:17037

1985

M. Finkelberg, Super Brauer group, Moscow Institute for Oil and Gas Industry ("Kerosinka").

See [B3].

1998

C. Bergelund, A. Szabo and G. Toth-Wessely, Valda problem från Moskvas matematiska olympiader, Stockholm University.

2009

M. Chapovalov, Explicit growth functions of the Coxeter groups of Lannér and quasi-Lannér type, Stockholm University.

See [100].

Last modified: Thu Mar 14 16:55:08 CET 2013