Structure of Algebras of Weyl Type

Abstract

In a recent paper by the authors, the associative and the Lie algebras of Weyl type 𝒜[𝒟] = 𝒜 ⊗ 𝔽[𝒟] were introduced, 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 and 𝒟 consisting of locally finite derivations of 𝒜, is studied. The isomorphism classes of these associative and Lie algebras are determined. The structure of these algebras is described explicitly.

Key Words:

• Lie algebra of Weyl type
• Associative algebra of Weyl type
• Derivation
• Isomorphism class

AMS Subject Classification:

• Primary: 17B20
• 17B65
• 17B67
• 17B68

Acknowledgments

This work is supported by a NSF grant 10171064 of China and two grants “Excellent Young Teacher Program” and “Trans-Century Training Programme Foundation for the Talents” from Ministry of Education of China.

Notes

^#Communicated by B. Allison.