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Noether's first variational theorem establishes a correspondence between symmetries and invariants. I would like to know what has been written on the following question: How do the invariants deform when we deform the symmetries? How about if the Lie algebra of symmetries is deformed as an L-infinity-algebra?

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    $\begingroup$ Hmm, the Lagrangian controls both the symmetries and the conserved currents and, as you say, provides an isomorphism between them via Nöther's first theorem. So if one is deformed, by isomorphism, the other follows suit. However, by definition, the symmetries of a Lagrangian AFAIK always remain a Lie algebra. Do you have an example of a non-Lie algebra deformation? $\endgroup$
    – Igor Khavkine
    Commented Sep 10, 2012 at 22:56

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