# 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 $k=\mathbb{C}$, then an algebraic torus is the complexification of the standard torus $(S^{1})^{n}$.

Title algebraic torus AlgebraicTorus 2013-03-22 13:53:27 2013-03-22 13:53:27 bwebste (988) bwebste (988) 7 bwebste (988) Definition msc 14L17