Cohomologies and deformations of right-symmetric algebras

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An algebra A with identity (a∘ b)∘ c-a∘(b∘ c)=(a∘ c)∘ b-a∘(c∘ b), is called right-symmetric. Cohomology and deformation theory for right-symmetric algebras are developed. Cohomologies of glₙ and half-Witt algebras Wₙrsym, p=0, Wₙrsym(m), p>0, are calculated. In particular, one right-symmetric central extension of W₁rsym is constructed.