Conformal super Virasoro algebra: Matrix model and quantum deformed algebra

In this paper, we construct the super Virasoro algebra with an arbitrary conformal dimension [Formula: see text] from the generalized [Formula: see text]-deformed quantum algebra and investigate the [Formula: see text]-deformed super Virasoro algebra with the particular conformal dimension [Formula: see text] Furthermore, we perform the [Formula: see text]-conformal Virasoro [Formula: see text]-algebra, the [Formula: see text]-conformal super Virasoro [Formula: see text]-algebra ([Formula: see text]-even) and discuss a toy model for the [Formula: see text]-conformal Virasoro constraints and [Formula: see text]-conformal super Virasoro constraints. Besides, we generalized the notion of the [Formula: see text]-elliptic Hermitian matrix model with an arbitrary conformal dimension [Formula: see text]. Finally, we deduce relevant particular cases generated by quantum algebras known in the literature.