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Noether identities of a generic differential operator. The Koszul-Tate complex

G. Sardanashvily
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Abstract

Given a generic Lagrangian system, its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy first-stage Noether identities, and so on. This construction is generalized to arbitrary differential operators on a smooth fiber bundle. Namely, if a certain necessary and sufficient condition holds, one can associate to a differential operator the exact chain complex with the boundary operator whose nilpotency condition restarts all the Noether identities characterizing the degeneracy of an original differential operator.

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G. Sardanashvily. 2005-06-09. Noether identities of a generic differential operator. The Koszul-Tate complex. https://arxiv.org/abs/math/0506103

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