Abstract
Abstract The aim of this paper is to study some brackets defined on (τ,σ)-derivations satisfying quasi-Lie identities. Moreover, we provide examples of ( p , q ) ${(p,q)}$ -deformations of Witt and Virasoro algebras as well as 𝔰 𝔩 $\mathfrak{sl}$ (2) algebra. These constructions generalize the results obtained by Hartwig, Larsson and Silvestrov on σ-derivations, arising in connection with discretizations and deformations of algebras of vector fields.
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