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So far fluid mechanical Nambu brackets have mainly been given on an intuitivebasis. Alternatively an algorithmic construction of such a bracket for thetwo-dimensional vorticity equation is presented here. Starting from theLie--Poisson form and its algebraic properties it is shown how the Namburepresentation can be explicitly constructed as the continuum limit from thestructure preserving Zeitlin discretization.

Algebraic construction of a Nambu bracket for the two-dimensional vorticity equation