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The second cohomology group of Lie algebras of kind L®U with trivial coefficients is investigated, where L admits a decomposition with onedimensional root spaces and U is an arbitrary associative commutative algebra with unit. This paper gives a unification of some recent results of C. Kassel and A. Haddi and provides a determination of central extensions of certain modular semisimple Lie algebras.doi:10.1090/s0002-9947-1992-1069751-2 fatcat:xn57iakhczhoza63oyqiyd6dqe