In one of our recent papers, the associative and the Lie algebras of Weyl type A[D] = A F[D] were defined and studied, where A is a commutative associative algebra with an identity element over a field F of any charac...In one of our recent papers, the associative and the Lie algebras of Weyl type A[D] = A F[D] were defined and studied, where A 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 subalgebra D of A. In the present paper, a class of the above associative and Lie algebras A[D] with F being a field of characteristic 0, D consisting of locally finite but not locally nilpotent derivations of A, are studied. The isomorphism classes and automorphism groups of these associative and Lie algebras are determined.展开更多
Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the...Poisson algebras are fundamental algebraic structures in physics and symplectic 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.展开更多
The ring of quaternion over R,denoted by R[i,j,k],is a quaternion algebra. In this paper,the roots of quadratic equation with one variable in quaternion field are investigated and it is shown that it has infinitely ma...The ring of quaternion over R,denoted by R[i,j,k],is a quaternion algebra. In this paper,the roots of quadratic equation with one variable in quaternion field are investigated and it is shown that it has infinitely many roots. Then the properties of quaternion algebra over Zp are discussed,and the order of its unit group is determined. Lastly,another ring isomorphism of M2（Zp） and the quaternion algebra over Zp when p satisfies some particular conditions are presented.展开更多
基金This work was supported by the National Natural Science Foundation of China,Hundred Talents Program of Chinese Academy of Sciences and a Fund from National Education Ministry of China. Su Yucai was partially supported by Academy of Mathematics and Syst
文摘In one of our recent papers, the associative and the Lie algebras of Weyl type A[D] = A F[D] were defined and studied, where A 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 subalgebra D of A. In the present paper, a class of the above associative and Lie algebras A[D] with F being a field of characteristic 0, D consisting of locally finite but not locally nilpotent derivations of A, are studied. The isomorphism classes and automorphism groups of these associative and Lie algebras are determined.
基金This work is supported by the National Natural Science Foundation of China (Grant No.10171064)two grants 'Excellent Young Teacher Program' and 'Trans-Century Training Programme Foundation for the Talents' from Ministry of Education of China.
文摘Poisson algebras are fundamental algebraic structures in physics and symplectic 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.
文摘The ring of quaternion over R,denoted by R[i,j,k],is a quaternion algebra. In this paper,the roots of quadratic equation with one variable in quaternion field are investigated and it is shown that it has infinitely many roots. Then the properties of quaternion algebra over Zp are discussed,and the order of its unit group is determined. Lastly,another ring isomorphism of M2（Zp） and the quaternion algebra over Zp when p satisfies some particular conditions are presented.
基金supported by NSFC(No.11701339,11871206,11871479,12071484)Hunan Provincial Natural Science Foundation(No.2020JJ5096,2018JJ2479,2020JJ4675)Shandong Province Natural Science Foundation of(No.ZR2018MA012)
