22-XX Topological groups, Lie groups {For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX}
22-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
22-01 Instructional exposition (textbooks, tutorial papers, etc.)
22-02 Research exposition (monographs, survey articles)
22-03 Historical {!must also be assigned at least one classification number from section 01}
22-04 Explicit machine computation and programs (not the theory of computation or programming)
22-06 Proceedings, conferences, collections, etc.
22Axx Topological and differentiable algebraic systems {For topological rings and fields, see 12Jxx, 13Jxx, 16W80}
22A05 Structure of general topological groups
22A10 Analysis on general topological groups
22A15 Structure of topological semigroups
22A20 Analysis on topological semigroups
22A22 Topological groupoids (including differentiable and Lie groupoids) [See also 58H05]
22A25 Representations of general topological groups and semigroups
22A26 Topological semilattices, lattices and applications [See also 06B30, 06B35, 06F30]
22A30 Other topological algebraic systems and their representations
22A99 None of the above, but in this section
22Bxx Locally compact Abelian groups (LCA groups)
22B05 General properties and structure of LCA groups
22B10 Structure of group algebras of LCA groups
22B99 None of the above, but in this section
22C05 Compact groups
22Dxx Locally compact groups and their algebras
22D05 General properties and structure of locally compact groups
22D10 Unitary representations of locally compact groups
22D12 Other representations of locally compact groups
22D15 Group algebras of locally compact groups
22D20 Representations of group algebras
22D25 C*-algebras and W*-algebras in relation to group representations [See also 46Lxx]
22D30 Induced representations
22D35 Duality theorems
22D40 Ergodic theory on groups [See also 28Dxx]
22D45 Automorphism groups of locally compact groups
22D99 None of the above, but in this section
22Exx Lie groups {For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis theorem, see 43A80, 43A85, 43A90}
22E05 Local Lie groups [See also 34-XX, 35-XX, 58H05]
22E10 General properties and structure of complex Lie groups [See also 32M05]
22E15 General properties and structure of real Lie groups
22E20 General properties and structure of other Lie groups
22E25 Nilpotent and solvable Lie groups
22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
22E30 Analysis on real and complex Lie groups [See also 33C80, 43-XX]
22E35 Analysis on p-adic Lie groups
22E40 Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
22E41 Continuous cohomology [See also 57R32, 57Txx, 58H10]
22E43 Structure and representation of the Lorentz group
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05}
22E46 Semisimple Lie groups and their representations
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]
22E50 Representations of Lie and linear algebraic groups over local fields [See also 20G05]
22E55 Representations of Lie and linear algebraic groups over global fields and ad\`ele rings [See also 20G05]
22E60 Lie algebras of Lie groups {For the algebraic theory of Lie algebras, see 17Bxx}
22E65 Infinite-dimensional Lie groups and their Lie algebras [See also 17B65, 58B25, 58H05]
22E67 Loop groups and related constructions, group-theoretic treatment [See also 58D05]
22E70 Applications of Lie groups to physics; explicit representations [See also 81R05, 81R10]
22E99 None of the above, but in this section
22Fxx Noncompact transformation groups
22F05 General theory of group and pseudogroup actions {For topological properties of spaces with an action, see 57S20}
22F10 Measurable group actions [See also 28Dxx and 22D40]
22F30 Homogeneous spaces {For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40}
22F50 Groups as automorphisms of other structures