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Yayın Cohomologies and generalized derivations of n-Lie algebras(Electronic Journals Project, 2022) Ateşli, Begüm; Esen, Oğul; Sütlü, SerkanA cohomology theory associated to an n-Lie algebra and a representation space of it is introduced. It is shown that this cohomology theory classifies generalized derivations of n-Lie algebras as 1-cocycles, and inner generalized derivations as 1-coboundaries.Yayın Cohomologies and generalized derivation extensions of n-Lie algebras(Cornell Univ, 2021-04-18) Ateşli, Begüm; Esen, Oğul; Sütlü, SerkanA cohomology theory, associated to a n-Lie algebra and a representation space of it, is introduced. It is observed that this cohomology theory is qualified to encode the generalized derivation extensions, and that it coincides, for n = 3, with the known cohomology of n-Lie algebras. The abelian extensions and infinitesimal deformations of n-Lie algebras, on the other hand, are shown to be characterized by the usual cohomology of n-Lie algebras. Furthermore, the Hochschild-Serre spectral sequence of the Lie algebra cohomology is upgraded to the level of n-Lie algebras, and is applied to the cohomology of generalized derivation extensions.
