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
|