Fire and the forge. He is the Greek god of blacksmiths, craftsmen.
Cerberus was not a ruler. It was the three-headed beast-guardian of the realm of Hades, Greek god of the underworld.
The Greek god of space is Uranus. In Greek mythology, Uranus is considered the personification of the sky and is the father of the Titans, who are the ancestors of the Greek gods. He plays a significant role in the creation of the universe and is often associated with the concept of the heavens and the celestial realm.
Tekhnê is a Greek goddess of art, and Hephaestus the Greek god of the art of sculpture/stone/metal-craft. Techne was less a goddess and more a personification. The arts were usually the realm of the Muses.
Ares, being a son of Zeus, didn't have his own realm (i.e. sky, underworld, ocean). He did have places that were sacred to him, and the Spartans, Myrmidons and Romans revered him most of all.
The underworld, the realm of the dead.
The Greek goddess Aphrodite was the goddess of love.
Hypnos was the god of sleep.
Apollo's realm was the sun, music, poetry, healing, and prophecy. He was also associated with truth, archery, and the arts. Apollo was considered one of the most important and multifaceted of the Greek gods.
Fire and the forge. He is the Greek god of blacksmiths, craftsmen.
Ares did not have a single kingdom or realm to rule. He was not a king. Ares was a Greek god.
Hades is the God of the Underworld, the dead, and riches. He protects the departed souls within his realm.
Apollo was the Greek god of light, music, and poetry. His realm was associated with the sun, healing, and prophecy. He was often depicted as an archer and a musician.
Ares did have a realm his was most feared on the war filed snice he was the the god of war
Hades is both the underworld in Greek mythology and the name of the god who presides over that realm.
Poseidon was a Greek god, god of the sea. He had no formal education, but would have become innately omniscient about his realm.
Poseidon is the god of the seas, creator of horses, etc. Basically, his domain is the oceans, the rivers, the lakes.