Cohomologies and deformations of right-symmetric algebras

An algebra $A$ with identity $(a\circ b)\circ c-a\circ(b\circ c)=(a\circ c)\circ b-a\circ(c\circ b),$ is called right-symmetric. Cohomology and deformation theory for right-symmetric algebras are developed. Cohomologies of $g{l}_n$ and half-Witt algebras $W_n^{rsym},p=0,$ $W_n^{rsym}(\mathbf{m}),p>0,$ are calculated. In particular, one right-symmetric central extension of $W_1^{rsym}$ is constructed.