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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 : More precisely, acts on by conjugation and two homomorphisms are defined to be equivalent 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. ==Formulation== Formally, and when the algebraic group is defined over the complex numbers , the -character variety is the spectrum of prime ideals of the ring of invariants : Here more generally one can consider algebraically closed fields of prime characteristic. In this generality, character varieties are only algebraic sets and are not actual varieties. To avoid technical issues, one often considers the associated reduced space by dividing by the radical of 0 (eliminating nilpotents). However, this does not necessarily yield an irreducible space either. Moreover, if we replace the complex group by a real group we may not even get an algebraic set. In particular, a maximal compact subgroup generally gives a semi-algebraic set. On the other hand, whenever is free we always get an honest variety; it is singular however. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「character variety」の詳細全文を読む スポンサード リンク
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