20Gxx Linear algebraic groups and related topics (For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55)
 20G05 Representation theory
 20G07 Structure theory
 20G10 Cohomology theory
 20G15 Linear algebraic groups over arbitrary fields

20G20 Linear algebraic groups over the reals, the complexes, the quaternions
(1)
 20G25 Linear algebraic groups over local fields and their integers

20G30 Linear algebraic groups over global fields and their integers
(1)
 20G35 Linear algebraic groups over adÃ¨les and other rings and schemes
 20G40 Linear algebraic groups over finite fields
 20G41 Exceptional groups
 20G42 Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]
 20G43 Schur and qSchur algebras
 20G44 KacMoody groups
 20G45 Applications to physics
 20G99 None of the above, but in this section