# Brackets with $(\tau,\sigma)$-derivations and $(p,q)$-deformations of Witt and Virasoro algebras

@article{Elchinger2014BracketsW, title={Brackets with \$(\tau,\sigma)\$-derivations and \$(p,q)\$-deformations of Witt and Virasoro algebras}, author={Olivier Elchinger and Karl Lundeng{\aa}rd and Abdenacer Makhlouf and Sergei D. Silvestrov}, journal={arXiv: Quantum Algebra}, year={2014} }

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.

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