We consider a semidirect product of the sheaf of vector fields on a manifold C* × X with a central extension of the sheaf of Lie algebras of maps from C* ×X into a finitedimensional simple Lie algebra, viewed as sheaves on X. Using vertex algebra methods we construct sheaves of modules for this sheaf of Lie algebras. Our results extend the work of Malikov-Schechtman-Vaintrob on the chiral de Rham complex.

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Keywords Chiral de Rham complex, Sheaf of Lie algebras, Vertex algebras
Persistent URL dx.doi.org/10.1142/S0129167X12500796
Journal International Journal of Mathematics
Billig, Y. (2012). Modules for a sheaf of lie algebras on loop manifolds. International Journal of Mathematics, 23(8). doi:10.1142/S0129167X12500796