For a nonassociative algebra R over a field k, we give a necessary and sufficient condition determining when sl2(R) is a Lie algebra and call such R sl2-Lie admissible.If R is sl2-Lie admissible and chark ≠2,sl2(R)is the universal covering algebra of sl2 (R), and H2(sl2(R),k) is studied.If R is associative, we characterize H2(sl2(R),k)and Prove H2(sl2(R),k) → H2(sl3(R),k) is surjective (not necessarily injective).Also, a class of sl2-Lie admissible algebras is constructed and as a byproduct, we get a realization of the Heisenberg Lie algebras.
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