Abstract
These notes are an informal introduction to algebras of chiral differential operators. The language used is one of vertex algebras, otherwise the approach chosen is that suggested by Beilinson and Drinfeld. The prerequisites are kept to a minimum, and we even give an informal introduction to the Beilinson-Bernstein localization theory in the example of the projective line.
Partially supported by an NSF grant.
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Notes
- 1.
This short-cut was suggested by V. Kac, who was in class.
- 2.
Pull-back w.r.t. the adjunction A → J ∞ A.
- 3.
In the formulas to follow, the summation w.r.t. the repeated indices is assumed.
- 4.
The reader will find more information on chiral Hamiltonian reduction in lectures by T. Arakawa in this volume.
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Malikov, F. (2017). An Introduction to Algebras of Chiral Differential Operators. In: Callegaro, F., Carnovale, G., Caselli, F., De Concini, C., De Sole, A. (eds) Perspectives in Lie Theory. Springer INdAM Series, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-58971-8_2
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