Novikov-Poisson algebras and associative commutative derivation algebras

We describe Novikov-Poisson algebras in which a Novikov algebra is not simple while its corresponding associative commutative derivation algebra is differentially simple. In particular, it is proved that a Novikov algebra is simple over a field of characteristic not 2 iff its associative commutative derivation algebra is differentially simple. The relationship is established between Novikov-Poisson algebras and Jordan superalgebras. Supported by RFBR (grant No. 05-01-00230), by SB RAS (Integration project No. 1.9), and by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (project NSh-344.2008.1). __________ Translated from Algebra i Logika, Vol. 47, No. 2, pp. 186–202, March–April, 2008.     

Jordan superalgebras with a solvable even part

In the article we show that a Jordan superalgebra over a ring with unity, containing an element 1/3, is solvable whenever its even part is solvable.Translated fromAlgebra i Logika, Vol. 34, No. 1, pp. 44–60, January–February, 1995.     

The Chevalley and Costant theorems for Mal’tsev algebras

Centers of universal envelopes for Mal’tsev algebras are explored. It is proved that the center of the universal envelope for a finite-dimensional semisimple Mal’tsev algebra over a field of characteristic 0 is a ring of polynomials in a finite number of variables equal to the dimension of its Cartan subalgebra, and that universal enveloping algebra is a free module over its center. Centers of universal enveloping algebras are computed for some Mal’tsev algebras of small dimensions. Supported by FAPESP grant No. 04/08537-4 and by SO RAN grant No. 1.9. Supported by FAPESP grant Nos. 05/60142-7, 05/60337-2 and by CNPq grant No. 304991/2006-6. __________ Translated from Algebra i Logika, Vol. 46, No. 5, pp. 560–584, September–October, 2007.     

The coradical of a Jordan (alternative) coalgebra and the quasiregular radical of its dual algebra

It is proved that the orthogonal complement to the coradical of a Jordan (alternative) coalgebra coincides with the quasiregular radical of the dual algebra.     

Universal envelopes of Malcev Algebras: Pointed Moufang bialgebras

Under study are the pointed unital coassociative cocommutative Moufang H-bialgebras. We prove an analog of the Cartier-Kostant-Milnor-Moore theorem for weakly associative Moufang H-bialgebras. If the primitive elements commute with group-like elements then these Moufang H-bialgebras are isomorphic to the tensor product of a universal enveloping algebra of a Malcev algebra and a loop algebra constructed by a Moufang loop.     

Simple Special Jordan Superalgebras with Associative Even Part

We describe the simple special unital Jordan superalgebras with associative even part A whose odd part M is an associative module over A. We prove that each of these superalgebras, not isomorphic to a superalgebra of nondegenerate bilinear superform, is isomorphically embedded into a twisted Jordan superalgebra of vector type. We exhibit a new example of a simple special Jordan superalgebra. We also describe the superalgebras such that M [A,M] 0.