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cyclic space in nLab


24 in nLab

The third stable homotopy group of spheres is the cyclic group of order 24. String theory. Critical Bosonic string theory requires 26 spacetime ...

rational vector space in nLab

1. Definition. A vector space/module over the field of rational numbers. Equivalently, a torsion-free divisible group. 2. Related concepts.

spectrum in nLab

Connective and non-connective spectra; infinite loop spaces ... As opposed to the homotopy groups of a topological space, the homotopy groups of a ...

orientation in nLab

Hochschild cohomology, cyclic cohomology · string topology ... A vector space always has an orientation, but a manifold or bundle may not.

C-star-algebra in nLab

Example 3.2. For A A a C * C^\ast -algebra and for X X a locally compact Hausdorff topological space, the set of continuous functions X → A X \to A which vanish ...

W*-category in nLab

cyclic vector, separating vector · modular theory · Fell's theorem ... admits a predual as a Banach space. That is, there is a Banach space ...

Gelfand duality in nLab

Every (nonunital) commutative C * C^\ast -algebra A A is equivalent to the C * C^\ast -algebra of continuous functions on the topological space ...

divisible group in nLab

Proposition 2.2. The torsion-free and divisible abelian groups are precisely the rational vector spaces, i.e. if A ...

Reeh-Schlieder theorem in nLab

The fact that the vacuum vector is cyclic means that any arbitrary state in the vacuum representation can be approximated by measurements in an ...

algebraic K-theory in nLab

Historically, the algebraic K-theory of a commutative ring R R (what today is the “0th” algebraic K-theory group) was originally defined to be ...

topological K-theory in nLab

Let X X be a pointed topological space, hence a topological space equipped with a choice of point x ∈ X x \in X , hence with a continuous ...

Alain Connes in nLab

Introducing the cyclic category and cyclic objects (cyclic sets, cyclic spaces) for cyclic homology: Alain Connes, Cohomologie cyclique et ...

state on a star-algebra in nLab

... space, become positive operators as defined here in the Hilbert space setting. ... cyclic vector ψ ∈ ℋ \psi \in \mathscr{H} as. ρ ( g ) ...

cocycle space in nLab

n-cells/n-morphisms are n n th order coboundaries (i.h. higher homotopies/higher gauge transformations). 2. Definition.

bounded operator in nLab

The Gelfand-Naimark theorem says that every C*-algebra is isomorphic to a C * C^\ast -algebra of bounded linear operators on a Hilbert space.

Introduction to Topological K-Theory in nLab

These are sequences of abelian groups which classify formal formal linear combinations of “singular chains” in a topological space, essentially ...

cohomology in nLab

H \mathbf{H} is the (∞,1)-category of G G -spaces for a compact Lie group G G and S \mathbf{S} is equivariant stable homotopy theory. In this ...

von Neumann algebra in nLab

Definition. A vector x ∈ ℋ x \in \mathcal{H} is a cyclic vector if ℳ x \mathcal{M}x is dense in ℋ \mathcal{H} .

geometry of physics -- fundamental super p-branes in nLab

... space is cyclic cohomology. \,. Shadows of this construction appear prominently also at other places in string theory notably in discussion ...

Gelfand-Naimark-Segal construction in nLab

a cyclic vector ψ ρ ∈ ℋ \psi_\rho ... and hence we have to quotient out by this null-space in order to produce the desired Hilbert space.