Eld Of Characteristic Zero Research Articles

ЧИСЛОВЫЕ ХАРАКТЕРИСТИКИ АЛГЕБР ЛЕЙБНИЦА-ПУАССОНА

The paper is survey of recent results of investigations on varieties of Leibniz-Poisson algebras. We show that a variety of Leibniz-Poisson algebras has either polynomial growth or growth with exponential not less than 2, the eld being arbitrary. We show that every variety of Leibniz-Poisson algebras of polynomial growth over a eld of characteristic zero has a nite basis for its polynomial identities.We construct a variety of Leibniz-Poisson algebras with almost polynomial growth. We give equivalent conditions of the polynomial codimension growth of a variety of Leibniz-Poisson algebras over a eld of characteristic zero. We show all varieties of Leibniz-Poisson algebras with almost polynomial growth in one class of varieties. We study varieties of Leibniz-Poisson algebras, whose ideals of identities contain the identity fx; yg fz; tg = 0, we study an interrelation between such varieties and varieties of Leibniz algebras. We show that from any Leibniz algebra L one can construct the Leibniz-Poisson algebra A and the properties of L are close to the properties of A. We show that if the ideal of identities of a Leibniz-Poisson variety V does not contain any Leibniz polynomial identity then V has overexponential growth of the codimensions. We construct a variety of Leibniz-Poisson algebras with almost exponential growth. Let f n(V)gn1 be the sequence of proper codimension growth of a variety of Leibniz-Poisson algebras V. We give one class of minimal varieties of Leibniz-Poisson algebras of polynomial growth of the sequence f n(V)gn1, i.e. the sequence of proper codimensions of any such variety grows as a polynomial of some degree k, but the sequence of proper codimensions of any proper subvariety grows as a polynomial of degree strictly less than k.

Series of Varieties of Lie Algebras of Different Fractional Exponents

We consider numerical characteristics of varieties of Lie algebras over a eld of characteristic zero and their polynomial identities. Here we have constructed an innite series of such varieties with dierent fractional exponents.

SAGBI bases for the Kernel of certain locally nilpotent K-derivations on polynomial rings.

In this paper is obtained an algebraic-computational property related to the theory of SAGBI bases for the specific case of the kernel of some locally nilpotent derivations on the polynomial ring in several variables over a eld of characteristic zero. The result achieved via explicit calculation is an algebraic characterization and a nite SAGBI basis for the kernel of a certain class of locally nilpotent derivations.

A theta divisor containing an abelian subvariety

We construct a Jacobian of dimension three whose theta divisor contains an elliptic curve. We work over an algebraically closed .eld of characteristic zero.

Polynomials dividing infinitely many quadrinomials or quintinomials

1. Introduction. In this paper we give necessary and sucien t conditions for polynomials in Q[x] having only simple roots to divide innitely many standard quadrinomials or quintinomials over Q. Let K be any eld of characteristic zero. A polynomial P 2 K[x] which is of the form P (x) = k X i=1 aix m i with m1 > ::: > mk 1 > mk = 0 and a1 = 1