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

References

Textbook accounts:

• Igor R. Shafarevich, Alexey O. Remizov: §4.3 in: Linear Algebra and Geometry (2012) [doi:10.1007/978-3-642-30994-6, MAA-review]

See also:

• Wikipedia, Complexification