Noncommutative Geometry (1994 book)
E286303
Noncommutative Geometry (1994 book) is Alain Connes’ foundational monograph that systematically develops the theory of noncommutative spaces and its applications to mathematics and theoretical physics.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Noncommutative Geometry (1994 book) canonical | 1 |
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics monograph
ⓘ
non-fiction book ⓘ |
| author | Alain Connes ⓘ |
| field |
functional analysis
ⓘ
mathematical physics ⓘ noncommutative geometry ⓘ operator algebras ⓘ |
| genre |
advanced mathematics textbook
ⓘ
research monograph ⓘ |
| hasMainConcept |
duality between spaces and commutative C*-algebras
ⓘ
extension of geometric notions to noncommutative algebras ⓘ noncommutative space as an operator algebra ⓘ use of spectral data to encode geometry ⓘ |
| influenced |
development of spectral action models in physics
ⓘ
research in index theory ⓘ research in mathematical formulations of the Standard Model ⓘ research in operator algebras ⓘ |
| language | English ⓘ |
| notableFor |
applications of noncommutative geometry to physics
ⓘ
foundational exposition of spectral triples ⓘ introduction of cyclic cohomology as a tool in noncommutative geometry ⓘ systematic development of noncommutative geometry ⓘ |
| publicationYear | 1994 ⓘ |
| subject |
C*-algebras
ⓘ
Chern character ⓘ
surface form:
Chern character in cyclic cohomology
Dirac operator ⓘ
surface form:
Dirac operators
Fredholm modules ⓘ K-theory ⓘ applications to gauge theory ⓘ applications to gravity ⓘ applications to particle physics ⓘ applications to the Standard Model of particle physics ⓘ cyclic cohomology ⓘ foliation C*-algebras ⓘ index theory ⓘ leaf spaces of foliations ⓘ local index formula ⓘ measure theory on noncommutative spaces ⓘ noncommutative integration ⓘ noncommutative spaces ⓘ noncommutative tori ⓘ quantum groups ⓘ spectral action principle ⓘ spectral triples ⓘ transverse geometry of foliations ⓘ von Neumann algebras ⓘ |
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Subject: Noncommutative Geometry (1994 book) Description of subject: Noncommutative Geometry (1994 book) is Alain Connes’ foundational monograph that systematically develops the theory of noncommutative spaces and its applications to mathematics and theoretical physics.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.