P. M. Lavrov, O. V. Radchenko, I. V. Tyutin
We present new basic identity for any associative algebra in terms of single commutator and anticommutators. From this identity we derive the set of four identities in terms of double commutators and anticommutators. Two of these four identities are independent. Equipping a given algebra with the basic identity we can prove that the multiplication in this algebra satisfies the associative condition. Extension of obtained results to supercase is found. A new identity for non-degenerate even symplectic (super)manifolds is proposed. Generalization of basic identity for the case of arbitrary number of elements is given.
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http://arxiv.org/abs/1304.5050
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