algebraic torus

Let $k$ be a field. Then $k^{*}$, the multiplicative group of $k$ is an affine algebraic group over $k$. An affine algebraic group of the form ${(k^{*})}^n$ is called an algebraic torus over $k$.

The name is to the fact that if $k=ℂ$, then an algebraic torus is the complexification of the standard torus ${(S^1)}^n$.