ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 17,18, 55 Dzhumadil’daev, Askar, Institute of Mathematics, Kazakhstan Cohomologies of right-symmetric algebras and Novikov algebras Right-symmetric identity is (a ∘ b) ∘ c − a ∘ (b ∘ c) = (a ∘ c) ∘ b − a ∘ (c ∘ b). Left-commutative identity is a ∘ (b ∘ c) = b ∘ (a ∘ c). Right-symmetric left commutative algebra is called Novikov. We develop cohomology theories for right-symmetric algebras, left-commutative algebras and, in particularly for Novikov algebras. We prove that they have pre-simplicial structures. We use our theory for constructing right-symmetric (Novikov) deformations and central extensions for matrix algebras and vector fields Lie algebras. We give also constructions Leibniz algebras by Novikov algebras.