On a construction of self-dual gauge fields in seven dimensions

We consider gauge fields associated with a semisimple Malcev algebra. We construct a gauge-invariant Lagrangian and found a solution of modified Yang-Mills equations in seven dimensions.Comment: 10 pages, LaTeX, no figure

Kimmerle conjecture for the Held and O'Nan sporadic simple groups

Using the Luthar--Passi method, we investigate the Zassenhaus and Kimmerle conjectures for normalized unit groups of integral group rings of the Held and O'Nan sporadic simple groups. We confirm the Kimmerle conjecture for the Held simple group and also derive for both groups some extra information relevant to the classical Zassenhaus conjecture

Description of costandard modules for Schur superalgebra S(2 vertical bar 1) in positive characteristic

We describe the characters of simple modules and composition factors of costandard modules for S(2 vertical bar 1) in positive characteristics and verify a conjecture of La Scala-Zubkov regarding polynomial superinvariants for GL(2 vertical bar 1)

Generators of supersymmetric polynomials in positive characteristic

In Kantor and Trishin (1997) [3], Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie superalgebra gl(m vertical bar n) and a related algebra A, of what they called pseudosymmetric polynomials over an algebraically closed field K of characteristic zero. The algebra A(s) was investigated earlier by Stembridge (1985) who in [9] called the elements of A(s) supersymmetric polynomials and determined generators of A(s). The case of positive characteristic p of the ground field K has been recently investigated by La Scala and Zubkov (in press) in [6]. We extend their work and give a complete description of generators of polynomial invariants of the adjoint action of the general linear supergroup GL(m vertical bar n) and generators of A(s)

Infinite dimensional Lie algebra associated with conformal transformations\ud of the two-point velocity correlation tensor from isotropic turbulence

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized\ud by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family\ud of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this\ud tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the\ud template for embedding the couple (K3, ds2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce\ud into the consideration the function of length between the fluid particles, and the accompanying important problem to\ud address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the\ud paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this\ud configuration and comment the case of a negative Gaussian curvature.This work was supported by FAPESP (grant No 11/50984-1), DFG Foundation (grant No OB 96/32-1) and partially by RFBR (grant No 11-01-12075-OFIM-2011)