
The second cohomology group of Lie algebras of kind L ⊗ U L \otimes U with trivial coefficients is investigated, where L L admits a decomposition with one-dimensional root spaces and U 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.
Modular Lie (super)algebras, central extensions, modular semisimple Lie algebras, second cohomology, Cohomology of Lie (super)algebras, cyclic cohomology
Modular Lie (super)algebras, central extensions, modular semisimple Lie algebras, second cohomology, Cohomology of Lie (super)algebras, cyclic cohomology
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