Mathematics Subject Classification 1991

22-XX Topological groups, Lie groups, {For transformation groups, See 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, See 43-XX} ( 0 Dok.)

• 22-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 22-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 22-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 22-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 22-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 22-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 22Axx Topological and differentiable algebraic systems, {For topological rings and fields, See 12Jxx, 13Jxx, 16W80; for dual spaces of operator algebras and topological groups, See 47D35} ( 0 Dok. )
• 22A05 Structure of general topological groups ( 0 Dok.)
• 22A10 Analysis on general topological groups ( 0 Dok.)
• 22A15 Structure of topological semigroups ( 0 Dok.)
• 22A20 Analysis on topological semigroups ( 0 Dok.)
• 22A22 Topological groupoids (including differentiable and Lie groupoids) ( 0 Dok.)
• 22A25 Representations of general topological groups and semigroups ( 0 Dok.)
• 22A26 Topological semilattices, lattices and applications, See also {06B30, 06B35, 06F30} ( 0 Dok.)
• 22A30 Other topological algebraic systems and their representations ( 0 Dok.)
• 22A99 None of the above but in this section ( 0 Dok.)
• 22Bxx Locally compact abelian groups (LCA groups) ( 0 Dok. )
• 22B05 General properties and structure of LCA groups ( 0 Dok.)
• 22B10 Structure of group algebras of LCA groups ( 0 Dok.)
• 22B99 None of the above but in this section ( 0 Dok.)
• 22C05 Compact groups ( 0 Dok.)
• 22Dxx Locally compact groups and their algebras ( 0 Dok. )
• 22D05 General properties and structure of locally compact groups ( 0 Dok.)
• 22D10 Unitary representations of locally compact groups ( 0 Dok.)
• 22D12 Other representations of locally compact groups ( 0 Dok.)
• 22D15 Group algebras of locally compact groups ( 0 Dok.)
• 22D20 Representations of group algebras ( 0 Dok.)
• 22D25 $C$*-algebras and $W$*-algebras arising from group representations, See also {46Lxx} ( 0 Dok.)
• 22D30 Induced representations ( 0 Dok.)
• 22D35 Duality theorems ( 0 Dok.)
• 22D40 Ergodic theory on groups, See also {28Dxx, 43A60} ( 0 Dok.)
• 22D45 Automorphism groups of locally compact groups ( 0 Dok.)
• 22D99 None of the above but in this section ( 0 Dok.)
• 22Exx Lie groups, {For the topology of Lie groups and homogeneous spaces, See {57-XX, 57Sxx, 57Txx}; for analysis thereon, See {43-XX, 43A80, 43A85, 43A90} ( 0 Dok. )
• 22E05 Local Lie groups, See also {34-XX, 35-XX, 58H05} ( 0 Dok.)
• 22E10 General properties and structure of complex Lie groups, See also {32M05} ( 0 Dok.)
• 22E15 General properties and structure of real Lie groups ( 0 Dok.)
• 22E20 General properties and structure of other Lie groups ( 0 Dok.)
• 22E25 Nilpotent and solvable Lie groups ( 0 Dok.)
• 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) ( 0 Dok.)
• 22E30 Analysis on real and complex Lie groups, See also {33C80, 43-XX} ( 0 Dok.)
• 22E35 Analysis on $p$-adic Lie groups, See also {11R56} ( 0 Dok.)
• 22E40 Discrete subgroups of Lie groups, See also {20Hxx, 32Nxx} ( 0 Dok.)
• 22E41 Continuous cohomology, See also {57R32, 57Txx, 58H10} ( 0 Dok.)
• 22E43 Structure and representation of the Lorentz group ( 0 Dok.)
• 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods, {For the purely algebraic theory, See 20G05} ( 0 Dok.)
• 22E46 Semisimple Lie groups and their representations ( 0 Dok.)
• 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.), See also {17B35} ( 0 Dok.)
• 22E50 Representations of Lie and linear algebraic groups over local fields ( 0 Dok.)
• 22E55 Representations of Lie and linear algebraic groups over global fields and adele rings, See also {20G05} ( 0 Dok.)
• 22E60 Lie algebras of Lie groups, {For the algebraic theory of Lie algebras, See 17Bxx} ( 0 Dok.)
• 22E65 Infinite-dimensional Lie groups and their Lie algebras, See also {17B65, 58B25, 58H05} ( 0 Dok.)
• 22E67 Loop groups and related constructions, group-theoretic treatment, See also {58D05} ( 0 Dok.)
• 22E70 Applications of Lie groups to physics; explicit representations, See also {81R05, 81R10} ( 0 Dok.)
• 22E99 None of the above but in this section ( 0 Dok.)