Category: Noncommutative geometry

Derived noncommutative algebraic geometry
In mathematics, derived noncommutative algebraic geometry, the derived version of noncommutative algebraic geometry, is the geometric study of derived categories and related constructions of triangula
JLO cocycle
In noncommutative geometry, the JLO cocycle is a cocycle (and thus defines a cohomology class) in entire cyclic cohomology. It is a non-commutative version of the classic Chern character of the conven
Spectral triple
In noncommutative geometry and related branches of mathematics and mathematical physics, a spectral triple is a set of data which encodes a geometric phenomenon in an analytic way. The definition typi
Quantum differential calculus
In quantum geometry or noncommutative geometry a quantum differential calculus or noncommutative differential structure on an algebra over a field means the specification of a space of differential fo
Banach bundle (non-commutative geometry)
In mathematics, a Banach bundle is a fiber bundle over a topological Hausdorff space, such that each fiber has the structure of a Banach space.
Noncommutative torus
In mathematics, and more specifically in the theory of C*-algebras, the noncommutative tori Aθ, also known as irrational rotation algebras for irrational values of θ, form a family of noncommutative C
Noncommutative residue
In mathematics, noncommutative residue, defined independently by M. and , is a certain trace on the algebra of pseudodifferential operators on a compact differentiable manifold that is expressed via a
Noncommutative algebraic geometry
Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry, that studies the geometric properties of formal duals of non-commutative alg
Field with one element
In mathematics, the field with one element is a suggestive name for an object that should behave similarly to a finite field with a single element, if such a field could exist. This object is denoted
Connection (algebraic framework)
Geometry of quantum systems (e.g.,noncommutative geometry and supergeometry) is mainlyphrased in algebraic terms of modules andalgebras. Connections on modules aregeneralization of a linear connection
Fredholm module
In noncommutative geometry, a Fredholm module is a mathematical structure used to quantize the differential calculus. Such a module is, up to trivial changes, the same as the abstract elliptic operato
Noncommutative geometry
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 noncommutativ
Noncommutative standard model
In theoretical particle physics, the non-commutative Standard Model (best known as Spectral Standard Model), is a model based on noncommutative geometry that unifies a modified form of general relativ
Noncommutative quantum field theory
In mathematical physics, noncommutative quantum field theory (or quantum field theory on noncommutative spacetime) is an application of noncommutative mathematics to the spacetime of quantum field the
Noncommutative measure and integration
Noncommutative measure and integration refers to the theory of weights, states, and traces on von Neumann algebras (Takesaki 1979 v. 2 p. 141).