Cite this article as:
Volokitina E. Y. Cohomology of the Lie Algebra of Vector Fields on Some One-dimensional Orbifold. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2013, vol. 13, iss. 3, pp. 14-28. DOI: https://doi.org/10.18500/1816-9791-2013-13-3-14-28
Cohomology of the Lie Algebra of Vector Fields on Some One-dimensional Orbifold
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
the cohomology algebra of the Lie algebra of vector fields on the orbifold is isomorphic to the tensor product of the exterior algebra
with two generators of degree one and the polynomial ring with one generator of degree two. To prove this result author used the
Gelfand–Fuchs method with some modifications
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