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In the present paper we determine for each parallelizable smooth compact manifold the second cohomology spaces of the Lie algebra of smooth vector fields on with values in the module . The case of is of particular interest since the gauge algebra of functions on with values in a finite-dimensional simple Lie algebra has the universal central extension with center , generalizing affine Kac-Moody algebras. The second cohomology classifies twists of the semidirect product of with the...
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