Dimitry Leites  Workouts of SoS, 19772003
[Books and chapters in books]
[Books edited]
[Books translated]
[Papers]
[Encyclopedia entries]
[Workouts of SoS]
Here is the list of workouts of Seminar on Supermanifolds (later
renamed, more appropriately, Seminar on Supersymmetries) or SoS
during 19772003 and preprinted in
Reports of the Department of Mathematics,
Stockholm University, Sweden.
The number N/yearn denotes SoSpreprint N published in year indicated as
nth report of the Department. Titles of several preprints differ from those of
published vershions; we provide with the published one.
Some results have, at least apparently, nothing to do with
supersymmetry and were preprinted here at the preglasnost time,
when some Soviet authors found it difficult or impossible to get
an official permission to publish their paper but were willing to
take a risk and preprint their result "illegally" but in English.
Label s marking a contribution means
"to be superized".
1/198621
Preface. Tentative table of contents.
D. Leites, Selected problems of supermanifold theory, 121.
T. Khovanova,
Lie superalgebra structure on eigenfunctions, and jets of the resolvent's kernel
near the diagonal of an \(n\)th order ordinary differential operator, 2239.
A. Radul, Superstring Schwarz derivative and the Bott cocycle, 4857.
T. Khovanova,
Kortewegde Vries superequation related to the Lie superalgebra of
NeveuSchwarz2 string theory, 5873.
s
V. Sokolov,
Finitedimensional subalgebras in \(K(30)\) and evolutionary equations, 7489.
2/198622
s
J. Bernstein and O. Schwarzman,
Complex crystallographic Coxeter groups and affine root systems;
id., Chevalley's theorem for the complex crystallographic groups, 66 pp.
3/198623
s
J. Bernstein and
S. Gindikin,
Four papers on integral geometry and Einstein equations, 61 pp.
4/198624
V. Drinfeld, Quantum groups, 132.
D. Gurevich,
Quantum YangBaxter equation and a generalization of the formal Lie theory,
33123.
For a bit shorter version, see:

The YangBaxter equation and the generalization of formal Lie theory,
Dokl. Akad. Nauk SSSR 288 (1986), no.4, 797801 (in Russian);
English translation: Soviet Math. Doklady 33 (1986), no.3, 758762.
MR 88b:58066
5/198625
s
B. Feigin and D. Fuchs, Representations of Virasoro algebra, 70 pp.
Published in:

Representation of Lie groups and Related Topics
(ed. A.M. Vershik and D.P. Zhelobenko),
Advanced Studies in Contemporary Mathematics, 7, Gordon and Breach, 1990,
465554. MR 92f:17034

B. Feigin and E. Frenkel, Semiinfinite Weil complex and the Virasoro algebra,
Comm. Math. Phys. 137 (1991), no.3, 617639;
Erratum: 147 (1992), no.3, 647648.
MR 92h:17028
6/1987
M. Antonets and A. Tsvetkov,
Algebras of random variables and their representations, 27 pp.
Published in:
 Selecta Math. Soviet. 8 (1989), no.3, 271289. MR 91a:28010
7/1987
S. Merkulov, Superconformal invariance of \(N=1\) supersymmetric theories, 20 pp.
8/1987
J. Donin,
Skew diagrams and decomposition into irreducible components of the exterior and
symmetric powers of the adjoint representations of \(GL(n)\) and \(GL(pq)\), 138.
Partly published in:

Decompositions of tensor products of representations of a symmetric group and
of symmetric and exterior powers of the adjoint representation of
\(\mathfrak{gl}(N)\),
Dokl. Akad. Nauk SSSR 303 (1988), no.6, 12961301 (in Russian);
English translation: Soviet Math. Dokl. 38 (1989), no.3, 654658.
MR 91b:17007

Decomposition of symmetric and exterior powers of the coadjoint representation
of \(\mathfrak{gl}(n)\) in the unstable case,
Funkts. Anal. Prilozh. 26 (1992), no.4, 7073
(in Russian); English translation:
Funct. Anal. Appl. 26 (1992), no.4, 287289.
MR 94c:17014
s
P. Grozman,
On bilinear covariant differential operators acting on the space of tensor
fields on a symplectic manifold, 3944.
A. Onishchik,
The action of Lie superalgebras of Cartan type on some split supermanifolds,
4553.
Published in:

Actions of Cartanlike Lie superalgebras on some supermanifolds,
Problems in group theory and in homological algebra, Yaroslavl State Univ.,
1989, 4249 (in Russian). MR 91k:58007
9/198713
J. Bernstein,
Two papers for pedestrians on representations of Lie algebras and Lie
superalgebras, 60 pp.

See
[E5] and
[E8], respectively.
10/198714
s
J. Bernstein and
S. Gelfand,
\(\Lambda(\Theta)\)modules and algebraic vector bundles on
\(\mathbb P(\Theta)\), 28 pp.
Partly published in:

S.I. Gelfand,
Sheaves on \(\mathbb P^n\) and problems in linear algebra, Appendix in:
C. Okonek, M. Schneider and H. Spindler,
Vector bundles on complex projective spaces,
translated from the English by V.Ya. Lin; translation edited and with a preface
by Yu.I. Manin, Mir, Moscow, 1984 (in Russian). MR 86i:14005
11/198715
Two papers on differential geometry:
J. Bernstein, Admissible complexes of curves, 115.
s
A. Goncharov, Generalized conformal structures on manifolds, 1670.
Published in:

Selecta Math. Soviet. 6 (1987), no.4, 307340. MR 89e:53050.

Generalizedconformal structures on manifolds,
Problems in group theory and homological algebra, Yaroslavl State Univ.,
1983, 99111 (in Russian). MR 87a:53064

Constructions of Weyl representations of some simple Lie algebras,
Funkts. Anal. Prilozh. 16 (1982), no.2, 7071 (in Russian);
English translation:
Funct. Anal. Appl. 16 (1982), no.2, 133135.
MR 84d:22023

Infinitesimal structures related to Hermitian symmetric spaces,
Funkts. Anal. Prilozh. 15 (1981), no.3, 8384
(in Russian); English translation:
Funct. Anal. Appl. 15 (1981), no.3, 221223.
MR 83k:32046
12/198716
O. Ogievetsky, Two papers on \(K_2\)functors for superalgebras, 30 pp.
13/198717
G. Ilyuta, On monodromy groups and Dynkin diagrams, 23 pp.
The result bridges singularities and root systems over \(\mathbb Z/2\);
to understand explicit relation with superroot systems is an open problem.
14/198718
M. Finkelberg, Graded algebras and Brauer groups, 30 pp.
15/198719
V. Lyubashenko, Vectorsymmetries, 77 pp.
For a bit shorter version, see:

Hopf algebras and vector symmetries,
Uspekhi Mat. Nauk 41 (1986), no.5, 185186
(in Russian); English translation:
Russ. Math. Surv. 41 (1986), no.5, 153154.
MR 88c:58007

The Berezinian in some monoidal categories,
Ukrain. Mat. Zh. 38 (1986), no.5, 588592
(in Russian); English translation:
Ukrain. Math. J. 38 (1986), no.5, 501505.
MR 88f:16016
16/198720
I. Gelfand and Yu. Daletskii, Lie superalgebras and Hamilton operators, 26 pp.
Partly published in:

I.M. Gelfand, Yu.L. Daletskii and B.L. Tsygan,
On a variant of noncommutative differential geometry,
Dokl. Akad. Nauk SSSR 308 (1989), no.6, 12931297 (in Russian),
English translation: Soviet Math. Dokl. 40 (1990), no.2, 422426.
MR 91j:58015

Yu.L. Daletskii, Lie superalgebras in a Hamiltonian operator theory,
Nonlinear and turbulent processes in physics, Vol. 3,
Harwood Academic Publ., Chur, 1984, 12891295.
MR 87e:58066
17/198723
I. Volichenko, Nonhomogeneous subalgebras of commutative superalgebras, 17 pp.
 Published as appendix in [68].
18/198724
V. Ginzburg,
Twisted cotangent bundles and twisted differential operators, 11 pp.
19/198725
F. Weinstein, Cohomology of braid groups, 120.
s
B. Feigin,
On cohomology of the Lie algebra of vector fields and of the current algebra,
2150.
Published in:
 Selecta Math. Soviet. 7 (1988), no.1, 4962. MR 90c:17026
20/198726
A. Onishchik, Transitive Lie superalgebras of vector fields, 121.
A. Serov, Vector fields on split supermanifolds, 2281.
Partly published in:

A.L. Onishchik and A.A. Serov,
Lie superalgebras of vector fields on splittable flag supermanifolds,
Dokl. Akad. Nauk SSSR 300 (1988), no.2, 284287 (in Russian);
English translation: Soviet Math. Dokl. 37 (1988), no.3, 652655.
MR 89i:32067
21/198726
V. Serganova and A. Vaintrob,
Simple singularities of functions on supermanifolds, 59 pp.
22/19884
A. Sergeev, Irreducible representations of solvable Lie superalgebras, 112.
V. Serganova, Automorphisms and real structures of Lie superalgebras, 1399.
Published in:

Automorphisms of simple Lie superalgebras,
Izv. Akad. Nauk SSSR Ser. Mat. 48 (1984), no.3, 585598
(in Russian); English translation:
Math. USSRIzv. 24 (1985), no.3, 539551.
MR 85k:17019

Outer automorphisms and real forms of KacMoody superalgebras,
Group theoretical methods in physics, Vol. 3,
Harwood Academic Publ., Chur, 1985, 639642. MR 90f:17041

Classification of simple real Lie superalgebras and symmetric superspaces,
Funkts. Anal. Prilozh. 17 (1983), no.3, 4654
(in Russian); English translation:
Funct. Anal. Appl. 17 (1983), no.3, 200207.
MR 85i:17023

Automorphisms of the Lie superalgebras of string theories,
Funkts. Anal. Prilozh. 19 (1985), no.3, 7576
(in Russian); English translation:
Funct. Anal. Appl. 19 (1985), no.3, 226228.
MR 87c:17030.
For details of the proof, see [E7].
V. Serganova, Super Weyl groups and dominant weights, 100132.
Used in:

G. Egorov, How to superize \(\mathfrak{gl}(\infty)\),
Topological and geometrical methods in field theory
(ed. J. Mickelsson and O. Pekonen), World Scientific, 1992, 135146.
MR 94c:17007
23/19885
Several papers on equations of mathematical physics, 76 pp.:
D. Gurevich,
Appendices to 4/1986.
Hecke symmetries and quantum determinants, 116.
D. Leites, Corrections to [29], 1718.
D. Leites and E. Poletaeva,
Two remarks on Lie superalgebras of string theories, 1922.
s
V. Ovsienko and O. Udalova,
Projective structures and infinitedimensional Lie algebras associated with
a contact manifold, 2359.
T. Khovanova and O. Udalova, Superversions of Miura transformations, 6066.
T. Khovanova,
SturmLiouville operators connected with superanalogs of Virasoro algebra,
6776.
 The last two papers see in [B7].
24/19886
A. Vaintrob, Deformations of complex structures on supervarieties, 144 pp.
25/19887
s
A. Rosenberg, Almost quotient categories, sheaves and localization, 181 pp.
26/19888
A. Rosenberg, Noncommutative affine semischemes and schemes, 317 pp.
Published in:

Noncommutative algebraic geometry and representations of quantized
algebras, Mathematics and its Applications, 330. Kluwer, 1995. xii+315 pp.
MR 97b:14004
Later additions:

Preprints MPIMBonn
199983,
199984,
2003110,
2003111,
2003112.
27/19889
s
I. Miklashevsky, Connections, conformal structures and Einstein equations,
31 pp.
28/198810
A. Radul, Algebrogeometric solutions to the super KadomtsevPetviashvili
hierarchy, 110.
s
B. Bloch, Instantons and superpotential for string theory on K3surfaces, 1116.
s
V. Lychagin, V. Rubtsov and I. Chekalov,
A classification of MongeAmpère equations, 1769.
29/198811
A. Tolpygo, Lie algebra cohomology, its weights and generating functions, 34 pp.
30/198813
Textbook on supermanifolds and Lie superalgebras.
Introduction (after Manin's [E6]), 123.
Chapter 0. Lectures on algebraic geometry
(by/after Manin's [E6]), 24157.
J. Bernstein, D. Leites and V. Shander, Algebra and calculus on supermanifolds,
158313.
31/198814
Continuation of
30/1988 with addenda to
22/1988,
25/1988,
26/1988.
J. Bernstein and D. Leites,
Algebra and calculus on supermanifolds, Chapters 35, 144, 135172.
V. Shander, Integration theory on supermanifolds, 45131.
Addendum to 22/1988 (Tables), 173187.
Addendum to 26/1988, 188234.
D. Leites and I. Shchepochkina,
On classification of simple infinite dimensional Lie superalgebras of vector
fields, 235278.
D. Leites, J.P. SerreI.L. Kantor relations of the classical Lie superalgebras,
279289.

Published in
[51] and
[58].
32/198815
I. Shchepochkina, Maximal subalgebras of classical Lie superalgebras, 143.
A. Sergeev,
Invariant functions and LaplaceCasimir operators on Lie superalgebras, 4495.

Published in
[S1],
[S2] and
[60].
33/19892
F. Weinstein, On birational automorphisms of SeveriBrauer surfaces, 14 pp.
34/198911
s
D. Gurevich, Algebraic aspects of the quantum YangBaxter equation, 147.
V. Serganova, Simple Volichenko algebras, 4852.
35/19909
s
M. Zhitomirskii,
Typical singularities of differential \(1\)forms and Pfaffian equations, 1285.
D. Leites and E. Poletaeva,
Analogues of the Riemannian structure on supermanifolds, 286296.
E. Poletaeva,
Structure functions on \((22)\)dimensional supermanifolds with either of the
differential forms
\(d\xi^{\frac{2\lambda 1}{1\lambda}}((1\lambda )dpdq + \lambda d\eta d\xi)\)
or
\(d\xi^{\frac{\lambda}{\lambda 2}}(dpdq + d\eta d\xi)\),
where \(\lambda \in \mathbb C\), 297304.
Workouts of SoS preprinted at
MPIMBonn
36/2003
E. Poletaeva, The analogs of Riemannian and Penrose tensor on supermanifolds,
Preprint MPIMBonn 200319;
arXiv:math/0510165, 71 pp.
37/2003
D. Leites and P. Grozman,
SuperLie and problems (to be)
solved with it,
Preprint MPIMBonn 200339,
61 pp.
Somewhat belatedly we have decided
let us save trees and put preprints in arXiv only.
Last modified: Sat Jan 18 07:28:25 BRST 2014