For 10 points, name this operation that reflects complex numbers across the real axis by taking "a plus
Treating this operation as an automorphism is the first step in constructing the adjoint representation of a Lie ("lee") group. Every irreducible representation of an abelian group is one-dimensional because this operation partitions abelian groups into single-member sets. Each column in a group's character table corresponds to an equivalence class under this operation. Two elements of the symmetric group are related by this operation if they have the same number of cycles of each length, since this operation permutes labels in cycle notation. For a group element A, the result of this operation is B A B-inverse for some group element B. Another operation known by this name is applied to the entries in a matrix while computing its Hermitian transpose. For 10 points, name this operation that reflects complex numbers across the real axis by taking "a plus b i" to "a minus b i."
Treating this operation as an automorphism is the first step in constructing the adjoint representation of a Lie ("lee") group.
conjugation [accept word forms such as conjugate or conjugating; accept complex conjugate] &lt;Other Science (Math)&gt;