Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Volokitina E. Y. Cohomology of the Lie Algebra of Vector Fields on Some One-dimensional Orbifold. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 3, pp. 14-28. DOI: 10.18500/1816-9791-2013-13-3-14-28

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
27.08.2013
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Russian
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UDC: 
501.1

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

Autors: 
Volokitina Evgeniya Yur'evna, Saratov State University
Abstract: 

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

References: 
  1. Volokitina Е. Y. Cohomology of Lie algebra of vector fields on S1/Z2. Izv. Sarat. Univ. N.S. Ser. Math. Mech. Inform., 2012. vol. 12, iss. 1, pp. 8–15 (in Russian).
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Received: 
20.02.2013
Accepted: 
12.07.2013
Published: 
30.08.2013
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