Generalized Witt and Witt n-algebras, Virasoro algebras and constraints, and KdV equations from R(p,q)-deformed quantum algebras

TL;DR

This paper generalizes classical algebraic structures like Witt and Virasoro algebras using R(p,q)-deformed quantum algebras, deriving related KdV equations and exploring their properties and applications.

Contribution

It introduces a generalized framework for Witt and Virasoro algebras based on R(p,q)-deformations, including new algebraic structures and constraints relevant to matrix models.

Findings

Derived generalized Witt and Virasoro algebras from R(p,q)-deformed quantum algebras

Constructed R(p,q)-deformed Witt n-algebra and Virasoro constraints

Provided explicit results for known deformed quantum algebras

Abstract

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, 063518, (2010). 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 matter of illustration, explicit results are provided for main particular deformed quantum algebras known in the literature.