Abstract
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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Communicated by Y. Kawahigashi
Dedicated to Corrado De Concini on his 60th birthday
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de Sole, A., Kac, V.G. Lie Conformal Algebra Cohomology and the Variational Complex. Commun. Math. Phys. 292, 667–719 (2009). https://doi.org/10.1007/s00220-009-0886-1
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DOI: https://doi.org/10.1007/s00220-009-0886-1