Yes, in Greek mythology, Hades is considered to be alive, or rather, existing, as he is an immortal god.
Hades, the god of the Underworld, is not subject to death in the same way mortals are. His immortality is a fundamental aspect of his divine nature. He maintains the balance of the Underworld and the imprisonment of the Titans in Tartarus, tasks only an immortal being could fulfill.
Even if Hades could die, the implications would be unclear. His realm is already the Underworld, the domain of the dead. Where would a deceased Hades go? The very nature of his existence is intertwined with the concept of being beyond death.
In short, Hades remains a constant figure in Greek mythology, eternally ruling his domain.
