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".


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.


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.


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


V. Drinfeld, Quantum groups, 1-32.

D. Gurevich, Quantum Yang-Baxter equation and a generalization of the formal Lie theory, 33-123.


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


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


S. Merkulov, Superconformal invariance of \(N=1\) supersymmetric theories, 20 pp.


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.


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


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


Two papers on differential geometry:

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


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


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.


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


V. Lyubashenko, Vectorsymmetries, 77 pp.


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


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


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


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.


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

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


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


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.


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.


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


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


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


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


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.


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


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.


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.


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


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


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


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


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


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