2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153840A hierarchy of first-degree time-dependent symmetries is proposed for Dirac soliton hierarchy and their commutator relations with time-dependent symmetries are exhibited. Meantime, a hereditary structure of Dirac soliton hierarchy is elucidated and a Lax operator algebra associated with Virasoro symmetry algebra is given.8 pages, latex, to appear in Inverse ProblemsExactly Solvable and Integrable Systemstext