Lie algebra

Connections of Nonzero Curvature on Three-dimensional Non-reductive Spaces

Authors: Mozhey N. P.

When a homogeneous space admits an invariant affine connection? If there exists at least one invariant connection then the space is isotropy-faithful, but the isotropy-faithfulness is not sufficient for the space in order to have invariantconnections. If a homogeneousspace is reductive, then the space admits an invariant connection.Thepurposeoftheworkisadescriptionofthree-dimensionalnon-reductivehomogeneousspaces, admitting invariant affine connections of nonzero curvature only, and the affine connections, curvature and torsion tensors.

Three-dimensional Homogeneous Spaces, Not Admitting Invariant Connections

Authors: Mozhey N. P.

The purpose of the work is the classification of three-dimensional isotropy-faithful homogeneous spaces, not admitting invariant connections. The local classification of homogeneous spaces is equivalent to the description of effective pairs of Lie algebras. If there exists at least one invariant connection then the space is isotropy-faithful, but the isotropy-faithfulness is not sufficient for the space in order to have invariant connections.

On the A. V. Mikhalev’s Problem for Lie Algebras

Authors: Mescherina E. V., Pikhtilkov S. A., Pikhtilkova O. A.

Weakened A. V. Mikhalev’ sproblem about the prime radical of artinian Lie algebras is solved.

Cohomology of Lie algebra of vector fields on S1/Z2

Authors: Volokitina E. Y.

 In the present paper we calculate the diagonal cohomology of Lie algebra of vector fields on S1/Z2 with coefficients in the space of smooth functions and 1-forms, one-dimensional and two-dimensional cohomology with coefficients in R. 

Cohomology of the Lie Algebra of Vector Fields on Some One-dimensional Orbifold

Authors: Volokitina E. Y.

I. M. Gelfand and D. B. Fuchs have proved that the cohomology algebra of the Lie algebra of vector fields on the unit circle is

isomorphic to the tensor product of the polynomial ring with one generator of degree two and the exterior algebra with one generator

of degree three. In the present paper the cohomology of the Lie algebra of vector fields on the one-dimensional orbifold S1/Z2 are

studied. S1/Z2 is the orbit space under the Z2 group action on the unit circle by reflection in the Ox axis. It has been proved that