Brackets with $(\tau,\sigma)$-derivations and $(p,q)$-deformations of   Witt and Virasoro algebras
  The aim of this paper is to study some brackets defined on $(\tau,\sigma)$-derivations satisfying quasi-Lie identities. Moreover, we provide examples of $(p,q)$-deformations of Witt and Virasoro algebras as well as $\mathfrak{sl}(2)$ algebra. These constructions generalize the results obtained by Hartwig, Larsson and Silvestrov on $\sigma$-derivations, arising in connection with discretizations and deformations of algebras of vector fields. 
Olivier Elchinger, Karl Lundengard, Abdenacer Makhlouf and Sergei D.   Silvestrov
math.QA math.RT