In mathematics, a Chevalley basis for a simple complex Lie algebra is a basis constructed by Claude Chevalley with the property that all structure constants are integers. Chevalley used these bases to construct analogues of Lie groups over finite fields, called Chevalley groups. The Chevalley basis is the Cartan-Weyl basis, but with a different normalization.

The generators of a Lie group are split into the generators H and E indexed by simple roots. The Cartan-Weyl basis may be written as

Defining the dual root or coroot as

is the euclidean inner product. One may perform a change of basis to define

The Cartan integers are

The resulting relations among the generators are the following:

is not a root.

an extraspecial pair is an extraspecial pair of roots. This then determines the signs for all remaining pairs of roots.

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