Characterization of the W1+∞-n-algebra and applications

In this paper, we construct the [Formula: see text]-n-algebras in the framework of the generalized quantum algebra. We characterize the [Formula: see text]-multi-variable [Formula: see text]-algebra and derive its n-algebra which is the generalized Lie algebra for n even. Furthermore, we investigate the [Formula: see text]-elliptic hermitian matrix model and determine a toy model for the generalized quantum [Formula: see text] constraints. Also, we deduce particular cases of our results.