cyclic space 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 ...
1. Definition. A vector space/module over the field of rational numbers. Equivalently, a torsion-free divisible group. 2. Related concepts.
Connective and non-connective spectra; infinite loop spaces ... As opposed to the homotopy groups of a topological space, the homotopy groups of a ...
Hochschild cohomology, cyclic cohomology · string topology ... A vector space always has an orientation, but a manifold or bundle may not.
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 ...
cyclic vector, separating vector · modular theory · Fell's theorem ... admits a predual as a Banach space. That is, there is a Banach space ...
Every (nonunital) commutative C * C^\ast -algebra A A is equivalent to the C * C^\ast -algebra of continuous functions on the topological space ...
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 ...
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 ...
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 ...
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 ) ...
n-cells/n-morphisms are n n th order coboundaries (i.h. higher homotopies/higher gauge transformations). 2. Definition.
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 ...
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 ...
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.