Simple Deformed Witt Algebras

Abstract

For any factorization domain $\mathcal{A}$ and an algebra endomorphism $\sigma$ of $\mathcal{A}$, there exists a non-associative algebra $(\mathcal{A},\sigma ,[\cdot ,\cdot ])$ with multiplication satisfying skew-symmetry and generalized (twisted) Jacobi identities, called a $\sigma$-deformed Witt algebra. In this paper, we obtain the necessary and sufficient conditions for the algebra $(\mathcal{A},\sigma ,[\cdot ,\cdot ])$ to be simple.

8 pages

References in corpus (4)

• Deformations of Lie Algebras using $\sigma$-derivations
• q-Witt Algebras, q-Virasoro algebra, q-Lie Algebras, q-Holomorph Structure and Representations
• Quantizations of the Witt algebra and of simple Lie algebras in characteristic p
• Some representations of nongraded Lie algebras of generalized Witt type