nLab 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