ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 17, 46 Ayupov, Shavkat Abdullaevich, Institute of Mathematics, Tashkent, Uzbekistan Nilpotent Leibniz algebras of low dimension. A Leibniz algebra L over a field F is an F-module equipped with a bilinear map called backet: [,] : L × L → L, satisfying the Leibniz identity: [x, [y, z]] = [[x, y], z] − [[x, z], y]. For Leibniz algebras the notions of right nilpotency and nilpotency coincide and mean that L^{<n>} = {0} for some natural n, where L^{<1>} = L, L^{<n+1>} = [L^{<n>}, L]. We give a description of 3 dimensional nilpotent Leibniz algebras,4-dimensional nilpotent Leibniz algebras with 1-dimensional right annihilator Z(L) = {x ∈ L : [y, x] = 0, for all y ∈ L} and some other classes of low dimensional nilpotent Leibniz algebras over the field with zero characteristic. Part of these results is joint work with Omirov. References: J. L. Loday, T. Pirashkili. Universal anveloping algebras of Leibniz algebras and (co)homology, Math. Ann. 296 (1993), 139-158.