Abstract
We perform generalizations of Witt and Virasoro algebras, and derive the corresponding Korteweg–de Vries equations from known [Formula: see text]-deformed quantum algebras previously introduced in J. Math. Phys. 51 (2010) 063518. Related relevant properties are investigated and discussed. Besides, we construct the [Formula: see text]-deformed Witt [Formula: see text]-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.
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