Isomorphism classes and automorphism groups of algebras of Weyl type

2000/12/03 by Yucai Su, Kaiming Zhao, Su, Yucai +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA

paper · pdf · doi:10.48550/arxiv.math/0012012

15 pages, Latex, to appear in Science in China A

arxiv created 2000/12/03 · arxiv updated 2009/11/30

Abstract

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.

Related

• Structure of Algebras of Weyl Type
• The group of automorphisms of the Lie algebra of derivations of a polynomial algebra
• Derivation-Simple Algebras and the Structures of Generalized Lie Algebras of Witt Type
• The relationship between local derivations and local automorphisms of some associative algebras
• Local derivations and automorphisms of nilpotent Lie algebra