We perform generalizations of Witt and Virasoro algebras, and derive the corresponding Korteweg–de Vries equations from known ℛ(p,q)-deformed quantum algebras previously introduced in J. Math. Phys. 51 (2010) 063518. Related relevant properties are investigated and discussed. Besides, we construct the ℛ(p,q)-deformed Witt n-algebra, and determine the Virasoro constraints for a toy model, which play an important role in the study of matrix models. Finally, as a matter of illustration, explicit results are provided for the main particular deformed quantum algebras known in the literature.

中文翻译：

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广义 Witt、Witt n 代数、Virasoro 代数和由 ℛ(p,q) 变形的量子代数导出的 KdV 方程

我们对 Witt 和 Virasoro 代数进行推广，并从已知的ℛ(p,q)-变形的量子代数先前在J.数学。物理。 51(2010) 063518. 对相关的相关性质进行了调查和讨论。此外，我们构建ℛ(p,q)-变形的威特n-代数，并确定玩具模型的 Virasoro 约束，这在矩阵模型的研究中起着重要作用。最后，作为说明，为文献中已知的主要特定变形量子代数提供了明确的结果。