linear algebraic group

A **linear algebraic group** $G$ is any algebraic subgroup of $GL(n,k)$ where $k$ is a field and $n$ a natural number.

An algebraic group is linear iff it is affine.

An algebraic group scheme is *affine* if the underlying scheme is affine.

The category of affine group schemes is the opposite of the category of commutative Hopf algebras.

- Armand Borel,
*Linear algebraic groups*, Springer - G. Hochschild,
*Algebraic groups and Hopf algebras*, Illinois J. Math.**14**:1 (1970), 52-65 euclid - Gerhard P. Hochschild,
*Basic theory of algebraic groups and Lie algebras*, Graduate Texts in Mathematics 75, 1981 doi - Akira Masuoka,
*Hopf algebraic techniques applied to super algebraic groups*, arXiv:1311.1261