Antibrackets and non-Abelian equivariant cohomology

The Weil algebra of a semisimple Lie group and an exterior algebra of a symplectic manifold possess antibrackets. They are applied to formulate the models of non--abelian equivariant cohomologies.Comment: 6 page

Massive 4d4d particle with torsion and conformal mechanics

The consequences of coupling of the torsion (highest curvature) term to the Lagrangian of a massive spinless particle in four-dimensional space-time are studied. It is shown that the modified system remains spinless and possesses extended gauge invariance. Though the torsion term does not generate spin, it provides the system with a nontrivial mass spectrum, described by one-dimensional conformal mechanics. Under an appropriate choise of characteristic constants the system has solutions with a discrete mass spectrum.Comment: 9 pages, revised version accepted in Phys.Lett.

Hessian K3 surfaces of non-Sylvester type

We construct the moduli space of cubic surfaces which do not admit a Sylvester form as an arithmetic quotient, and determine the graded ring of modular forms of even weights

Multi-center MICZ-Kepler systems

We present the classical solutions of the two-center MICZ-Kepler and MICZ-Kepler-Stark systems. Then we suggest the model of multi-center MICZ-Kepler system on the curved spaces equipped with $so(3)$-invariant conformal flat metrics.Comment: 7 pages, typos corrected, refs added. Contribution to the Proceedings of International Workshop on Classical and Quantum Integrable systems, 24-28.01.2007, Dubna, Russi