An embedding theorem for lattice-ordered fields

The Hahn Embedding Theorem for Abelian Lattice-ordered Groups

An embedding theorem for Hilbert categories

We axiomatically define (pre-)Hilbert categories. The axioms resemble those for monoidal Abelian categories with the addition of an involutive functor. We then prove embedding theorems: any locally small pre-Hilbert category whose monoidal unit is a simple generator embeds (weakly) monoidally into the category of pre-Hilbert spaces and adjointable maps, preserving adjoint morphisms and all fini...

An embedding theorem for Eichler orders

Let B be a quaternion algebra over number field K : Assume that B satisfies the Eichler condition (i.e., there is at least one archimedean place which is unramified in B). Let O be an order in a quadratic extension L of K: The Eichler orders of B which admit an embedding of O are determined. This is a generalization of Chinburg and Friedman’s embedding theorem for maximal orders. r 2004 Elsevie...

An embedding theorem for convex fuzzy sets

In this paper we embed the space of upper semicontinuous convex fuzzy sets on a Banach space into a space of continuous functions on a compact space. The following structures are preserved by the embedding: convex cone, metric, sup-semilattice. The indicator function of the unit ball is mapped to the constant function 1. Two applications are presented: strong laws of large numbers for fuzzy ran...

Density matrix embedding from broken symmetry lattice mean fields

Several variants of the recently proposed density matrix embedding theory (DMET) [G. Knizia and G. K-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)] are formulated and tested. We show that spin symmetry breaking of the lattice mean-field allows precise control of the lattice and fragment filling while providing very good agreement between predicted properties and exact results. We present a rigor...