Dimitry Leites - Workouts of SoS, 1977-2003

[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 1977-2003 and preprinted in Reports of the Department of Mathematics, Stockholm University, Sweden. The number N/year-n denotes SoS-preprint N published in year indicated as n-th 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 pre-glasnost 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".

1/1986-21

Preface. Tentative table of contents.

D. Leites, Selected problems of supermanifold theory, 1-21.
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, 22-39.
A. Radul, Superstring Schwarz derivative and the Bott cocycle, 48-57.
T. Khovanova, Korteweg-de Vries superequation related to the Lie superalgebra of Neveu-Schwarz-2 string theory, 58-73.
s V. Sokolov, Finite-dimensional subalgebras in \(K(3|0)\) and evolutionary equations, 74-89.

2/1986-22

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.

3/1986-23

 s J. Bernstein and S. Gindikin, Four papers on integral geometry and Einstein equations, 61 pp.

4/1986-24

V. Drinfeld, Quantum groups, 1-32.
D. Gurevich, Quantum Yang-Baxter equation and a generalization of the formal Lie theory, 33-123.

5/1986-25

s B. Feigin and D. Fuchs, Representations of Virasoro algebra, 70 pp.

6/1987

M. Antonets and A. Tsvetkov, Algebras of random variables and their representations, 27 pp.

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 \(GL(p|q)\), 1-38.
s P. Grozman, On bilinear covariant differential operators acting on the space of tensor fields on a symplectic manifold, 39-44.
A. Onishchik, The action of Lie superalgebras of Cartan type on some split supermanifolds, 45-53.

9/1987-13

J. Bernstein, Two papers for pedestrians on representations of Lie algebras and Lie superalgebras, 60 pp.

10/1987-14

s J. Bernstein and S. Gelfand, \(\Lambda(\Theta)\)-modules and algebraic vector bundles on \(\mathbb P(\Theta)\), 28 pp.

11/1987-15

Two papers on differential geometry:

J. Bernstein, Admissible complexes of curves, 1-15.
s A. Goncharov, Generalized conformal structures on manifolds, 16-70.

12/1987-16

O. Ogievetsky, Two papers on \(K_2\)-functors for superalgebras, 30 pp.

13/1987-17

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.

14/1987-18

M. Finkelberg, Graded algebras and Brauer groups, 30 pp.

15/1987-19

V. Lyubashenko, Vectorsymmetries, 77 pp.

16/1987-20

I. Gelfand and Yu. Daletskii, Lie superalgebras and Hamilton operators, 26 pp.

17/1987-23

I. Volichenko, Nonhomogeneous subalgebras of commutative superalgebras, 17 pp.

18/1987-24

V. Ginzburg, Twisted cotangent bundles and twisted differential operators, 11 pp.

19/1987-25

F. Weinstein, Cohomology of braid groups, 1-20.

s B. Feigin, On cohomology of the Lie algebra of vector fields and of the current algebra, 21-50.

20/1987-26

A. Onishchik, Transitive Lie superalgebras of vector fields, 1-21.

A. Serov, Vector fields on split supermanifolds, 22-81.

21/1987-26

V. Serganova and A. Vaintrob, Simple singularities of functions on supermanifolds, 59 pp.

22/1988-4

 A. Sergeev, Irreducible representations of solvable Lie superalgebras, 1-12.
V. Serganova, Automorphisms and real structures of Lie superalgebras, 13-99.
V. Serganova, Super Weyl groups and dominant weights, 100-132.

23/1988-5

Several papers on equations of mathematical physics, 76 pp.:

D. Gurevich, Appendices to 4/1986. Hecke symmetries and quantum determinants, 1-16.

D. Leites, Corrections to [29], 17-18.

D. Leites and E. Poletaeva, Two remarks on Lie superalgebras of string theories, 19-22.
s V. Ovsienko and O. Udalova, Projective structures and infinite-dimensional Lie algebras associated with a contact manifold, 23-59.

T. Khovanova and O. Udalova, Superversions of Miura transformations, 60-66.

T. Khovanova, Sturm-Liouville operators connected with superanalogs of Virasoro algebra, 67-76.

24/1988-6

A. Vaintrob, Deformations of complex structures on supervarieties, 144 pp.

25/1988-7

 s A. Rosenberg, Almost quotient categories, sheaves and localization, 181 pp.


26/1988-8

 A. Rosenberg, Noncommutative affine semischemes and schemes, 317 pp.

27/1988-9

s I. Miklashevsky, Connections, conformal structures and Einstein equations, 31 pp.

28/1988-10

A. Radul, Algebro-geometric solutions to the super Kadomtsev-Petviashvili hierarchy, 1-10.

s B. Bloch, Instantons and superpotential for string theory on K3-surfaces, 11-16.

s V. Lychagin, V. Rubtsov and I. Chekalov, A classification of Monge-Ampère equations, 17-69.

29/1988-11

A. Tolpygo, Lie algebra cohomology, its weights and generating functions, 34 pp.

30/1988-13

 Textbook on supermanifolds and Lie superalgebras. Introduction (after Manin's [E6]), 1-23.

Chapter 0. Lectures on algebraic geometry (by/after Manin's [E6]), 24-157.

J. Bernstein, D. Leites and V. Shander, Algebra and calculus on supermanifolds, 158-313.


31/1988-14

 Continuation of 30/1988 with addenda to 22/1988, 25/1988, 26/1988.

J. Bernstein and D. Leites, Algebra and calculus on supermanifolds, Chapters 3-5, 1-44, 135-172.

V. Shander, Integration theory on supermanifolds, 45-131.

Addendum to 22/1988 (Tables), 173-187.

Addendum to 26/1988, 188-234.

D. Leites and I. Shchepochkina, On classification of simple infinite dimensional Lie superalgebras of vector fields, 235-278.
D. Leites, J.P. Serre-I.L. Kantor relations of the classical Lie superalgebras, 279-289.

32/1988-15

I. Shchepochkina, Maximal subalgebras of classical Lie superalgebras, 1-43.
A. Sergeev, Invariant functions and Laplace-Casimir operators on Lie superalgebras, 44-95.

33/1989-2

F. Weinstein, On birational automorphisms of Severi-Brauer surfaces, 14 pp.


34/1989-11

s D. Gurevich, Algebraic aspects of the quantum Yang-Baxter equation, 1-47.
V. Serganova, Simple Volichenko algebras, 48-52.

35/1990-9

s M. Zhitomirskii, Typical singularities of differential \(1\)-forms and Pfaffian equations, 1-285.
D. Leites and E. Poletaeva, Analogues of the Riemannian structure on supermanifolds, 286-296.
E. Poletaeva, Structure functions on \((2|2)\)-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 \(\lambda \in \mathbb C\), 297-304.

Workouts of SoS preprinted at MPIM-Bonn

36/2003

 E. Poletaeva, The analogs of Riemannian and Penrose tensor on supermanifolds, Preprint MPIM-Bonn 2003-19; arXiv:math/0510165, 71 pp.

37/2003

D. Leites and P. Grozman, SuperLie and problems (to be) solved with it, Preprint MPIM-Bonn 2003-39, 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