Ui
Arturo Ui is the central character in the play as he comes to take over Chicago and Cicero in the 1930s. He is a metaphor for Adolf Hitler and the rise of the Nazi party in 1930s Germany.
Trust
The Cauliflower Trust is a group of men who seek to ensure their business continue to make profits in 1930s Chicago at the expense of the people of the city. This Trust is a metaphor for the Prussian Junkers who were a group of wealthy landowners who inherited vast lands on which peasants worked with very little rights.
Cicero
Cicero is a city outside of Chicago with Ui takes control of after gaining complete dominance over Chicago. Cicero is a metaphor for Austria, who would join the Third Reich after being terrorized with death by Hitler before a vote.
Shakespeare
Ui is given lessons in sitting, standing, walking and speaking by a Shakespearean actor. This is a metaphor for Hitler himself having hired an actor to train him in public speaking during his rise in Germany during the 1930s. We even see most of Brecht's text is written in iambic pentameter, a poetic verse that Shakespeare wrote in. This is a metaphor for how Ui's words were all speeches that were calculated and crafted, just like Hitler.
Moustache
The actor playing Arturo Ui takes off his mustache and addresses the audience directly in the last speech of the play. This is a metaphor for the fact that what Brecht's theatre is presenting is not merely entertainment, but a parable to learn from the very recent history in order that it doesn't happen again.