Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions, possibly in some generalized sense. A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which does not always equal ; or more generally an algebraic structure in which one of the principal binary operations is not commutative; one also allows additional structures, e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions.
An approach giving deep insight about noncommutative spaces is through operator algebras, that is, algebras of bounded linear operators on a Hilbert space.[1] Perhaps one of the typical examples of a noncommutative space is the "noncommutative torus", which played a key role in the early development of this field in 1980s and lead to noncommutative versions of vector bundles, connections, curvature, etc.[2]
^Khalkhali & Marcolli 2008, p. 171.
^Khalkhali & Marcolli 2008, p. 21.
and 25 Related for: Noncommutative geometry information
Noncommutativegeometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces...
Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutativegeometry, that studies the geometric...
identities. Commutative rings are much better understood than noncommutative ones. Algebraic geometry and algebraic number theory, which provide many natural...
theory that is an outgrowth of noncommutativegeometry and index theory in which the coordinate functions are noncommutative. One commonly studied version...
Anabelian geometry is a theory in number theory which describes the way in which the algebraic fundamental group G of a certain arithmetic variety X, or...
has described a relationship between the Riemann hypothesis and noncommutativegeometry, and showed that a suitable analog of the Selberg trace formula...
known for his contributions to the study of operator algebras and noncommutativegeometry. He is a professor at the Collège de France, Institut des Hautes...
described mathematically using the noncommutativegeometry of Connes, quantum geometry, or quantum groups. Any noncommutative algebra with at least four generators...
Absolute geometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally...
mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus. Annulus: a ring-shaped object, the region bounded...
less important theories include Causal dynamical triangulation, Noncommutativegeometry, and Twistor theory. One of the difficulties of formulating a quantum...
In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance...
Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two-dimensional surface of a sphere or the n-dimensional surface of...
system is useful. Noncommutativegeometry Ashtekar, Abhay; Corichi, Alejandro; Zapata, José A. (1998), "Quantum theory of geometry. III. Non-commutativity...
C*-algebras. Noncommutative topology is related to analytic noncommutativegeometry. The premise behind noncommutative topology is that a noncommutative C*-algebra...
Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land', and μέτρον (métron) 'a measure') is a branch of mathematics...
In their paper on string theory and noncommutativegeometry, Seiberg and Witten studied certain noncommutative quantum field theories that arise as limits...
planes over noncommutative rings had likely desensitized Dirac. In more advanced work, Dirac used extensive drawings in projective geometry to understand...
(2012). "Intersecting Quantum Gravity with NoncommutativeGeometry – a Review". Symmetry, Integrability and Geometry: Methods and Applications. 8: 018. arXiv:1203...
hand, and noncommutativegeometry on the other hand. It quickly led to the discovery of other important links between noncommutativegeometry and various...
the philosophy of noncommutativegeometry, which tries to study various non-classical and/or pathological objects by noncommutative operator algebras...
In geometry, the circumference (from Latin circumferens, meaning "carrying around") is the perimeter of a circle or ellipse. The circumference is the arc...
In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It...
Global Information
