Central character

Given a group $𝐺$ , a central character $𝜒 : 𝑍 (𝐺) \to 𝕂 \times$ is a linear character for its centre. #m/def/rep A general group representation $Γ : 𝐺 \to G L (𝑉)$ over $𝕂$ is said to have central character iff $𝑍 (𝐺)$ is represented as the centre of the general linear group $𝑍 (𝑉) ≅ 𝕂 \times$ , in which case the corresponding homomorphism is the corresponding central character.