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The standard formulation of two dimensional $N=(2,2)$ and $N=(0,2)$ supersymmetry algebras in physics is an explicit one; I am not aware of the underlying abstract Lie superalgebras. Does anyone know what these alegrbras are in terms of Lie superalgebras?

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Check the following:

http://www.ams.org/bookstore-getitem/item=FLS

http://www.ams.org/bookstore-getitem/item=QFT-1-2-S

http://arxiv.org/abs/hep-th/0106122

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