This is a large field, and now basic in the theories of algebraic groups.

These were the first algebraic groups to be extensively studied.

The decomposition is important in the study of algebraic groups.

He also introduced the algebraic group concept, which was not to be developed seriously before 1950.

More generally, this holds for simple algebraic groups of rank at least two over a local field.

His main publications were on quadratic forms and algebraic groups.

He is known for his work on representation theory, in particular for algebraic groups.

The circle group is more than just an abstract algebraic group.

Note that the degree is n 1 which agrees with the dimension as an algebraic group.

Ree groups are not given as the points of some connected algebraic group with values in a field.

The adjoint representation can also be defined for algebraic groups over any field.

There are a number of mathematical notions to study and classify algebraic groups.

Lie theory is frequently built upon a study of the classical linear algebraic groups.

The applications are mostly in number theory, particularly to adelic algebraic groups.

The direct Tamagawa number definition works well only for linear algebraic groups.

Only in 1948 did he prove that complete algebraic groups can be embedded into projective space.

There are similar problems with the points of other algebraic groups with values in finite fields.

He was a mathematician noted for his work on the decidability of various algebraic groups.

In fact, the unitary group is a linear algebraic group.

In the sequel, G denotes an algebraic group over a field k.

It is also in fact an algebraic group, since the composition involves only polynomial operations.

G is a connected, reductive algebraic group over an algebraically closed field.

Important examples are linear algebraic groups over finite fields.

Every direct sum of simple algebraic groups is semisimple.

Suppose that G is an algebraic group defined over a field k, such as the reals.