Generalized super- <i>W</i> 1+∞- <i>n</i> -algebra and Landau problem

We investigate the R(p,q)-super n-bracket and study their properties such that the generalized super Jacobi identity. Furthermore, from the R(p,q)-operators in a Supersymmetric Landau problem, we furnish the R(p,q)-super W1+∞ n-algebra which obey the generalized super Jacobi identity for n even. Also, we derive the R(p,q)-super W1+∞ sub-2n-algebra and deduce particular cases induced by quantum algebras existing in the literature.