Statements (190)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
gptkb:mathematical_concept Mathematical Structure |
| gptkbp:alsoKnownAs |
W*-algebra
|
| gptkbp:alternativeName |
Banach_algebra
Fredholm_module Operator_Algebra operator_algebra vertex_operator_algebra von_Neumann_algebra |
| gptkbp:appearsIn |
gptkb:cyclic_cohomology
gptkb:Baum–Connes_conjecture index theory |
| gptkbp:application |
gptkb:quantum_field_theory
gptkb:Quantum_Mechanics ergodic theory mathematical physics noncommutative geometry quantum mechanics representation theory algebraic combinatorics modular invariance representation of finite groups |
| gptkbp:closed |
adjoint operation
strong operator topology weak operator topology |
| gptkbp:contains |
identity operator
|
| gptkbp:containsElement |
identity element (sometimes)
|
| gptkbp:definedIn |
Banach algebra with involution satisfying the C*-identity
|
| gptkbp:defines |
gptkb:Hilbert_space
compact operator an associative algebra A over the real or complex numbers that is also a Banach space, such that the norm satisfies ||xy|| ≤ ||x||·||y|| for all x, y in A bounded operator representation of C*-algebra A *-subalgebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. |
| gptkbp:developedBy |
gptkb:John_von_Neumann
gptkb:Francis_J._Murray |
| gptkbp:example |
gptkb:lattice_vertex_operator_algebra
gptkb:moonshine_module gptkb:L^1_group_algebra algebra of bounded operators on a Hilbert space algebra of continuous functions on a compact space affine Lie algebra VOA |
| gptkbp:field |
gptkb:mathematics
gptkb:theoretical_physics gptkb:C*-algebra functional analysis operator algebras |
| gptkbp:fieldOfStudy |
gptkb:Mathematics
|
| gptkbp:generalizes |
gptkb:Fredholm_operator
gptkb:vertex_algebra gptkb:C*-algebra gptkb:commutative_C*-algebra normed algebra |
| gptkbp:hasApplication |
gptkb:C*-algebras
harmonic analysis operator theory spectral theory |
| gptkbp:hasAxiom |
locality
associativity Virasoro algebra action grading by conformal weight translation operator vacuum vector |
| gptkbp:hasProperty |
self-adjoint
associative multiplication can be finite or infinite complete normed vector space submultiplicative norm can be non-abelian closed under adjoint operation norm-closed unital closed in weak operator topology C*-identity: ||a*a|| = ||a||^2 subalgebra of bounded operators on Hilbert space can be a factor can be abelian can be properly infinite can be semifinite can be type I, II, or III can have a center can have a trace closed in strong operator topology contains commutant contains identity contains projections |
| gptkbp:hasSubfield |
gptkb:AF-algebra
gptkb:CAR_algebra gptkb:Cuntz_algebra gptkb:UHF_algebra gptkb:approximately_finite-dimensional_C*-algebra gptkb:commutative_C*-algebra gptkb:full_group_C*-algebra gptkb:non-unital_C*-algebra gptkb:nuclear_C*-algebra gptkb:reduced_group_C*-algebra gptkb:simple_C*-algebra gptkb:type_III_C*-algebra gptkb:type_II_C*-algebra gptkb:type_I_C*-algebra gptkb:unital_C*-algebra gptkb:Toeplitz_algebra functional analysis commutative Banach algebra non-commutative Banach algebra Functional Analysis C(X) for compact Hausdorff space X complex C*-algebra continuous function algebra crossed product C*-algebra factor C*-algebra finite-dimensional C*-algebra group C*-algebra infinite-dimensional C*-algebra matrix algebra over C*-algebra non-self-adjoint C*-algebra non-separable C*-algebra noncommutative C*-algebra prime C*-algebra primitive C*-algebra real C*-algebra self-adjoint C*-algebra separable C*-algebra |
| gptkbp:hasType |
gptkb:type_III_von_Neumann_algebra
gptkb:type_II_von_Neumann_algebra gptkb:type_I_von_Neumann_algebra gptkb:even_Fredholm_module gptkb:odd_Fredholm_module factor |
| https://www.w3.org/2000/01/rdf-schema#label |
C*-algebra
|
| gptkbp:includes |
gptkb:C*-algebra
gptkb:Von_Neumann_Algebra |
| gptkbp:introduced |
gptkb:John_von_Neumann
gptkb:Francis_J._Murray gptkb:Alain_Connes gptkb:Richard_Borcherds |
| gptkbp:introducedIn |
1930s
1940s 1986 |
| gptkbp:isA |
gptkb:Hilbert_space
algebra over a field |
| gptkbp:namedAfter |
gptkb:John_von_Neumann
gptkb:Stefan_Banach C |
| gptkbp:relatedTo |
gptkb:Fredholm_operator
gptkb:Hilbert_space gptkb:center gptkb:quantum_field_theory gptkb:Gelfand–Naimark_theorem gptkb:monstrous_moonshine_conjecture gptkb:vertex_algebra gptkb:C*-algebra gptkb:string_theory gptkb:Hilbert_Space gptkb:Gelfand_representation gptkb:modular_tensor_category gptkb:K-homology gptkb:Spectral_Theory gptkb:Noncommutative_Geometry modular forms representation theory spectral theory factor commutative Banach algebra projection trace modular invariance operator product expansion commutant |
| gptkbp:studiedBy |
gptkb:John_von_Neumann
gptkb:Francis_J._Murray gptkb:Arne_Meurman gptkb:Igor_Frenkel gptkb:James_Lepowsky functional analysts |
| gptkbp:studies |
States
Projections Representations Algebras of Linear Operators Automorphisms Bounded Linear Operators Commutators Unbounded Operators |
| gptkbp:usedIn |
gptkb:monstrous_moonshine
noncommutative geometry moonshine theory |
| gptkbp:bfsParent |
gptkb:Hilbert_space
gptkb:quantum_field_theory |
| gptkbp:bfsLayer |
4
|