nLab complexification

Idea

For $V$ a vector space over the real numbers or some other $\mathbb{R}$-module, its complexification is the tensor product over $\mathbb{R}$ with the complex numbers $\mathbb{C}$: the extension of scalars along the canonical inclusion $\mathbb{R} \hookrightarrow \mathbb{C}$.

Related concepts

• complex Lie algebra, complex Lie group