Noncommutative geometry (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 noncommutative geometry, that studies the geometric...

theory that is an outgrowth of noncommutative geometry and index theory in which the coordinate functions are noncommutative. One commonly studied version...

hand, and noncommutative geometry on the other hand. It quickly led to the discovery of other important links between noncommutative geometry and various...

identities. Commutative rings are much better understood than noncommutative ones. Algebraic geometry and algebraic number theory, which provide many natural...

has described a relationship between the Riemann hypothesis and noncommutative geometry, and showed that a suitable analog of the Selberg trace formula...

known for his contributions to the study of operator algebras and noncommutative geometry. He was a professor at the Collège de France, Institut des Hautes...

right Ore domain. Derived algebraic geometry Noncommutative geometry Noncommutative algebraic geometry Noncommutative harmonic analysis Representation theory...

described mathematically using the noncommutative geometry of Connes, quantum geometry, or quantum groups. Any noncommutative algebra with at least four generators...

geometry Noncommutative algebraic geometry Noncommutative geometry Ordered geometry Parabolic geometry Plane geometry Projective geometry Quantum geometry Riemannian...

(best known as Spectral Standard Model ), is a model based on noncommutative geometry that unifies a modified form of general relativity with the Standard...

C*-algebras. Noncommutative topology is related to analytic noncommutative geometry. The premise behind noncommutative topology is that a noncommutative C*-algebra...

hand, and noncommutative geometry on the other hand. It quickly led to the discovery of other important links between noncommutative geometry and various...

is useful. Noncommutative geometry Quantum spacetime Ashtekar, Abhay; Corichi, Alejandro; Zapata, José A. (1998), "Quantum theory of geometry. III. Non-commutativity...

Chamseddine developed the structures needed to define Riemannian noncommutative geometry (metric, connection and curvature) by applying this method to a...

In noncommutative geometry and related branches of mathematics and mathematical physics, a spectral triple is a set of data which encodes a geometric...

Geometry of quantum systems (e.g., noncommutative geometry and supergeometry) is mainly phrased in algebraic terms of modules and algebras. Connections...

less important theories include causal dynamical triangulation, noncommutative geometry, and twistor theory. One of the difficulties of formulating a quantum...

hand, and noncommutative geometry on the other hand. It quickly led to the discovery of other important links between noncommutative geometry and various...

considered fundamental in mainstream geometry and topology, there are some systems that forgo it, e.g. noncommutative geometry and pointless topology. A "pointless"...

discipline which draws upon methods of homological algebra, as does the noncommutative geometry of Alain Connes. Homological algebra began to be studied in its...

Arithmetic Noncommutative Geometry. American Mathematical Society. ISBN 9780821838334. Connes, Alain; Marcolli, Matilde (2008). Noncommutative Geometry, Quantum...

In quantum geometry or noncommutative geometry a quantum differential calculus or noncommutative differential structure on an algebra A {\displaystyle...

pure mathematics for insight into homological mirror symmetry and noncommutative geometry. The word "brane" originated in 1987 as a contraction of "membrane"...

the philosophy of noncommutative geometry, which tries to study various non-classical and/or pathological objects by noncommutative operator algebras...

symmetries in projective geometry and the combinatorics of simplicial complexes. F1 has been connected to noncommutative geometry and to a possible proof...

local arithmetic dynamics Noncommutative algebra Noncommutative algebraic geometry a direction in noncommutative geometry studying the geometric properties...

recent proposal in this direction by Penrose in 2015 was based on noncommutative geometry on twistor space and referred to as palatial twistor theory. The...

mathematics, noncommutative projective geometry is a noncommutative analog of projective geometry in the setting of noncommutative algebraic geometry. The quantum...

In noncommutative geometry and related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative...