Journal of Nonlinear Mathematical Physics

Volume 17, Issue Supplement 1, December 2010

Research Article

2. Bosonization Method for Second Super Quantization

Alexander Dynin
Pages: 1 - 13
A boson-fermion correspondence allows an analytic definition of functional super derivative, in particular, and a bosonic functional calculus, in general, on Bargmann Gelfand triples for the second super quantization. A Feynman integral for the super transformation matrix elements in terms of bosonic...
Research Article

3. Solutions of Burgers, Reynolds, and Navier–Stokes Equations via Stochastic Perturbations of Inviscid Flows

Yuri E. Gliklikh
Pages: 15 - 29
We show that a certain stochastic perturbation of the flow of perfect incompressible fluid under some special external force on the flat n-dimensional torus yields a solution of Navier–Stokes equation without external force in the tangent space at unit of volume preserving diffeomorphism group. If that...
Research Article

4. Bilinear Identities on Schur Symmetric Functions

Dimitri Gurevich, Pavel Pyatov, Pavel Saponov
Pages: 31 - 48
A series of bilinear identities on the Schur symmetric functions is obtained with the use of Plücker relations.
Research Article

5. On Invariants of Immersions of an n-Dimensional Manifold in an n-Dimensional Pseudo-Euclidean Space*

Djavvat Khadjiev
Pages: 49 - 70
Let Epn be the n-dimensional pseudo-Euclidean space of index p and M(n, p) the group of all transformations of Epn generated by pseudo-orthogonal transformations and parallel translations. We describe the system of generators of the differential field of all M(n, p)-invariant differential...
Research Article

6. On Stochastic Deformations of Dynamical Systems

Ilya Shereshevskii
Pages: 71 - 85
I discuss the connection of the three different questions: The existence of the Gibbs steady state distributions for the stochastic differential equations, the notion and the existence of the conservation laws for such equations, and the convergence of the smooth random perturbations of dynamical systems...
Research Article

7. Invariants of Lie Algebras Extended Over Commutative Algebras Without Unit

Pasha Zusmanovich
Pages: 87 - 102
We establish results about the second cohomology with coefficients in the trivial module, symmetric invariant bilinear forms, and derivations of a Lie algebra extended over a commutative associative algebra without unit. These results provide a simple unified approach to a number of questions treated...
Research Article

8. The Classification of Almost Affine (Hyperbolic) Lie Superalgebras

Danil Chapovalov, Maxim Chapovalov, Alexei Lebedev, Dimitry Leites
Pages: 103 - 161
We say that an indecomposable Cartan matrix A with entries in the ground field is almost affine if the Lie (super)algebra determined by it is not finite dimensional or affine (Kac–Moody) but the Lie sub(super)algebra determined by any submatrix of A, obtained by striking out any row and any column intersecting...
Research Article

9. Defining Relations of Almost Affine (Hyperbolic) Lie Superalgebras

Sofian Bouarroudj, Pavel Grozman, Dimitry Leites
Pages: 163 - 168
For all almost affine (hyperbolic) Lie superalgebras, the defining relations are computed in terms of their Chevalley generators.
Research Article

10. The Poincaré Series of the Hyperbolic Coxeter Groups with Finite Volume of Fundamental Domains

Maxim Chapovalov, Dimitry Leites, Rafael Stekolshchik
Pages: 169 - 215
The discrete group generated by reflections of the sphere, or the Euclidean space, or hyperbolic space are said to be Coxeter groups of, respectively, spherical, or Euclidean, or hyperbolic type. The hyperbolic Coxeter groups are said to be (quasi-)Lannér if the tiles covering the space are of finite...
Research Article

11. Analogs of the Orthogonal, Hamiltonian, Poisson, and Contact Lie Superalgebras in Characteristic 2

Alexei Lebedev
Pages: 217 - 251
Over algebraically closed fields of characteristic 2, the analogs of the orthogonal, symplectic, Hamiltonian, Poisson, and contact Lie superalgebras are described. The number of non-isomorphic types, and several properties of these algebras are unexpected, for example, interpretation in terms of exterior...
Research Article

12. Prolongs of (Ortho-)Orthogonal Lie (Super)Algebras in Characteristic 2

Uma N. Iyer, Alexei Lebedev, Dimitry Leites
Pages: 253 - 309
Cartan described some of the finite dimensional simple Lie algebras and three of the four series of simple infinite dimensional vectorial Lie algebras with polynomial coefficients as prolongs, which now bear his name. The rest of the simple Lie algebras of these two types (finite dimensional and vectorial)...
Research Article

13. Examples of Simple Vectorial Lie Algebras in Characteristic 2

Uma N. Iyer, Dimitry Leites, Mohamed Messaoudene, Irina Shchepochkina
Pages: 311 - 374
The classification of simple finite dimensional modular Lie algebras over algebraically closed fields of characteristic p > 3 (described by the generalized Kostrikin–Shafarevich conjecture) being completed due to Block, Wilson, Premet and Strade (with contributions from other researchers) the next...
Research Article

14. Infinite-Dimensional and Colored Supermanifolds

Vladimir Molotkov
Pages: 375 - 446
Here the theory of finite-dimensional supermanifolds is generalized in two directions. First, we introduce infinite-dimensional supermanifolds “locally isomorphic” to arbitrary Banach (or, more generally, locally convex) superspaces. This is achieved by considering supermanifolds as functors (equipped...