Derivations of a Restricted Weyl-Type Algebra Containing the Polynomial Ring

Abstract

A Weyl type nonassociative algebra and its subalgebra have been defined in the articles Choi and Nam (2005a b c); Lee and Nam (2004). Several authors have found all the derivations of some given algebra (see Ahmadi et al., 2005; Choi and Nam, 2005b; Kac, 1974; Kirkman et al., 1994; Osborn, 1997; Osborn and Passman, 1995). In this article, we find all derivations of the nonassociative algebra and show that the dimension of all derivations of the algebra is (s ₁ + s ₂)² + s ₁ + s ₂. Because of the dimension of a derivation algebra, we know that if s ₁ + s ₂ ≠ s ₁′ + s ₂′, then the algebras and are not isomorphic.

Key Words:

• Annihilator
• Derivation
• Idempotent
• Kronecker delta
• Non-associative algebra
• Right identity
• Simple

2000 Mathematics Subject Classification:

• Primary 17B40
• 17B56

Notes

Communicated by L. Ein.