Gelfand-Fuchs cohomology of invariant formal vector fields

Ilya Shapiro, Xiang Tang
2008 Mathematical Research Letters  
Let Γ be a finite group acting linearly on a vector space V . We compute the Lie algebra cohomology of the Lie algebra of Γ-invariant formal vector fields on V . We use this computation to define characteristic classes for foliations on orbifolds. 2.1. Eigenvalues of the Euler field. We point out that the Γ action on V can be made unitary 3 . Accordingly, as unitary representations of Γ are completely reducible, 1 This notation is a possible source of confusion as it is also used to denote the
more » ... used to denote the cyclic group generated by γ, however its meaning is clear from the context. 2 Note that M γ may have quite different connected components. 3 Had Γ not been a finite or more generally compact group, the condition that the action be unitary would have to be required.
doi:10.4310/mrl.2008.v15.n1.a12 fatcat:y6ihspb6rzd2vdjexar4x3o24a