2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51526We propose two non-abelian Chern-Simons matrix models as the effective descriptions of 4-dimensional quantum Hall fluids. One of them describes a new type of 4-dimensional quantum Hall fluid on the space of quaternions, the other provides the description of non-commutative field theory for Zhang and Hu's 4-dimensional quantum Hall fluid of $S^4$. The complete sets of physical quantum states of these matrix models are determined, and the properties of quantum Hall fluids related with them are discussed.4 pages, no figures, revtex, replaced by new versionHigh Energy Physics - TheoryMesoscale and Nanoscale Physicstext