In mathematical group theory, the root datum of a connected split reductive algebraic group over a field is a generalization of a root system that determines the group up to isomorphism. They were introduced by Michel Demazure in SGA III, published in 1970.

A root datum consists of a quadruple

where

The elements of ${\displaystyle \Phi }$ are called the roots of the root datum, and the elements of ${\displaystyle \Phi ^{\vee }}$ are called the coroots.

If ${\displaystyle \Phi }$ does not contain ${\displaystyle 2\alpha }$ for any ${\displaystyle \alpha \in \Phi }$, then the root datum is called reduced.

If ${\displaystyle G}$ is a reductive algebraic group over an algebraically closed field ${\displaystyle K}$ with a split maximal torus ${\displaystyle T}$ then its root datum is a quadruple

where

A connected split reductive algebraic group over ${\displaystyle K}$ is uniquely determined (up to isomorphism) by its root datum, which is always reduced. Conversely for any root datum there is a reductive algebraic group. A root datum contains slightly more information than the Dynkin diagram, because it also determines the center of the group.