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In this paper, we establish an explicit classification of length twoextensions of tensor modules for the Witt algebra using the cohomology of theWitt algebra with coefficients in the module of the space of homomorphismsbetween the two modules of interest. To do this we extended our module to amodule that has a compatible action of the commutative algebra of Laurentpolynomials in one variable. In this setting, we are be able to directlycompute all possible 1-cocycles.

Length two extensions of modules for the Witt Algebra