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
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.
