Isomorphism classes and automorphism groups of algebras of Weyl type

In one of our recent papers, the associative and the Lie algebras of Weyl typeAD]=A⊗FD] were defined and studied, whereA is a commutative associative algebra with an identity element over a field F of any characteristic, and FD] is the polynomial algebra of a commutative derivation subalgebraD ofA. In the present paper, a class of the above associative and Lie algebrasAD] 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