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1.
Isomorphism classes and automorphism groups of algebras of Weyl type   总被引:6,自引:0,他引:6  
In one of our recent papers, the associative and the Lie algebras of Weyl typeA[D]=A⊗F[D] were defined and studied, whereA is a commutative associative algebra with an identity element over a field F of any characteristic, and F[D] is the polynomial algebra of a commutative derivation subalgebraD ofA. In the present paper, a class of the above associative and Lie algebrasA[D] with F being a field of characteristic 0,D consisting of locally finite but not locally nilpotent derivations ofA, are studied. The isomorphism classes and automorphism groups of these associative and Lie algebras are determined  相似文献
2.
Central simple Poisson algebras   总被引:1,自引:0,他引:1  
Poisson algebras are fundamental algebraic structures in physics and sym-plectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero. The Lie algebra structures of these Poisson algebras are in general not finitely-graded.  相似文献
3.
In this paper we study the computation of the number of isomorphism classes of hyperelliptic curves of genus 2 over finite fields Fq with q even. We show the formula of the number of isomorphism classes, that is, for q = 2m, if 4 m, then the formula is 2q3 q2 - q; if 4 | m, then the formula is 2q3 q2 - q 8. These results can be used in the classification problems and the hyperelliptic curve cryptosystems.  相似文献
4.
We give the number and representatives of isomorphism classes of hyperelliptic curves of genus g defined over finite fields , g=1,2,3. These results have applications to hyperelliptic curve cryptography.  相似文献
5.
1987年,R.Schoof对于有限域Fq上的椭圆曲线的同构类数目得出了一个公式.1990年,A.M enezes和S.V anstone对此当q为偶数时给出了一个初等证明.本文利用Burnside引理对q为偶数时给出一个更简单的证明.  相似文献
6.
Let F be an algebracially closed field of characteristic p > 2, and L be the p n -dimensional Zassenhaus algebra with the maximal invariant subalgebra L 0 and the standard filtration {L i }| pn−2 i =−1. Then the number of isomorphism classes of simple L-modules is equal to that of simple L 0-modules, corresponding to an arbitrary character of L except when its height is biggest. As to the number corresponding to the exception there was an earlier result saying that it is not bigger than p n . Received May 10, 1999, Accepted December 8, 1999  相似文献
7.
Given a finite set A of integral vectors and a parameter vector, Gel'fand, Kapranov, and Zelevinskii defined a system of differential equations, called an A-hypergeometric (or a GKZ hypergeometric) system. Classifying the parameters according to the D-isomorphism classes of their corresponding A-hypergeometric systems is one of the most fundamental problems in the theory. In this paper we give a combinatorial answer for the problem under the assumption that the finite set A lies in a hyperplane off the origin, and illustrate it in two particularly simple cases: the normal case and the monomial curve case.  相似文献
8.
蔡迎春 《数学学报》1994,37(4):523-533
设n,k为自然数,G(n)阶群中的同构类数,Fk(x)与Qk(x)分别表示不超过x的自然数中使G(n)=k的自然数、无平方因子自然数的个数.本文的目的是用Brun筛法证明Qk(x)的条件渐近公式并对Fk(x)的渐近性质做出了推测.  相似文献
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