# Non-compact group, finite dimensional representation, and unitary representation

Are the following statements true about non-compact (Lie) group?

1. Non-compact group, for every finite dimensional representation $$Rightarrow$$ must be nonunitary representation

(naively, $$p Rightarrow q$$)

1. Non-compact group, for every unitary representation $$Rightarrow$$ must be infinite dimensional representation

(naively, $$sim q Rightarrow sim p$$)

1. Non-compact group, for every nonunitary representation $$Rightarrow$$ must be finite dimensional representation

(naively, $$q Rightarrow p$$)

1. Non-compact group, for every finite dimensional representation $$Rightarrow$$ must be nonunitary representation

(naively, $$sim p Rightarrow sim q$$)