Simon
Simon is the main character from the In the Machine, the story which takes place in Industrial Revolution-era New York. One day, when he is working in the factory, he is accidentally sucked into a machine which crushes him to death. Simon returns in Like Beauty as an AI, a living robot.
Lucas
Lucas is another main character of In the Machine. After Simon is sucked into the machine and vanishes, Lucas is sent to work in the factory in his place. He has a strange quirk where he randomly spouts the words of Leaves of Grass, a poetry collection by Walt Whitman. Lucas is scared of Simon's ghost, who he believes haunts not only the machine which killed him, but all the machines of the Industrial era.
Cat
Cat is the protagonist of The Children's Crusade, the second short story in the book. As a radio operator in the aftermath of 9/11, Cat fields calls everyday listening to people who also threaten to take violent measures against the government. Through her eyes, we witness the turn of events as a new terrorist group threatens New York.