Lie Conformal Algebra Cohomology and the Variational Complex

  title={Lie Conformal Algebra Cohomology and the Variational Complex},
  author={Alberto De Sole and Victor G. Kac},
  journal={Communications in Mathematical Physics},
  • A. Sole, V. Kac
  • Published 29 December 2008
  • Mathematics
  • Communications in Mathematical Physics
We find an interpretation of the complex of variational calculus in terms of the Lie conformal algebra cohomology theory. This leads to a better understanding of both theories. In particular, we give an explicit construction of the Lie conformal algebra cohomology complex, and endow it with a structure of a $${\mathfrak{g}}$$-complex. On the other hand, we give an explicit construction of the complex of variational calculus in terms of skew-symmetric poly-differential operators. 
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