Mathematics

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2005, No. 6



L.E. Abanina, S.M. Ratseev

MANIFOLD OF THE LEIBNIZ ALGEBRAS ASSOCIATED WITH STANDARD IDENTITIES

Let K be a field of characteristic zero. In this paper the manifold of the Leibniz algebras connected with associative Grassmann algebra is studied. It is prooved that the variety has almost polynomial growth and is the unique smallest variety in which no standard identity holds. The basis of the space of multilinear identities , basis of the identities of and a complete description of in the language of Young diagrams through the representation theory of the symmetric group ъръ are given.


E.A. Savinov, S.Ya. Shatskikh

CENTRAL LIMIT THEOREM FOR RANDOM VARIABLES GENERATED BY CONDITIONAL DISTRIBUTIONS OF A SIGMA-ADDITIVE CAUCHY MEASURE

The paper is devoted to the study of a triangular array scheme of asymptotically independent random variables generated by finite-dimensional conditional distributions of a sigma-additive Cauchy measure, defined on real Hilbert space. In the case, when the dimension of conditional distributions approaches infinity, the central limit theorem for triangular array scheme is proved.