In the mathematics of moduli theory, given an algebraic, reductive, Lie group and a finitely generated group , the -character variety of is a space of equivalence classes of group homomorphisms from to : More precisely, acts on by conjugation, and two homomorphisms are defined to be equivalent (denoted ) if and only if their orbit closures intersect. This is the weakest equivalence relation on the set of conjugation orbits, , that yields a Hausdorff space.
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