20Gxx 
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Linear algebraic groups (classical groups) 

{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 20G10 Cohomology theory 20G15 Linear algebraic groups over arbitrary fields 20G20 Linear algebraic groups over the reals, the complexes, the quaternions 20G25 Linear algebraic groups over local fields and their integers 20G30 Linear algebraic groups over global fields and their integers 20G35 Linear algebraic groups over adèles and other rings and schemes 20G40 Linear algebraic groups over finite fields 20G42 Quantum groups (quantized function algebras) and their representations [See also 16W35, 17B37, 81R50] 20G45 Applications to physics 20G99 None of the above, but in this section