Related papers: Classical structures of CP maps are all canonical

Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…

This is the continuation of Montes' paper "On the canonical discussion of polynomial systems with parameters". In this paper we define the Minimal Canonical Comprehensive Groebner System (MCCGS) of a parametric ideal and fix under which…

In this paper, we take a pervasively effectful (in the style of ML) typed lambda calculus, and show how to extend it to permit capturing pure expressions with types. Our key observation is that, just as the pure simply-typed lambda calculus…

We prove that for every singular cardinal mu of cofinality omega, the complete Boolean algebra compP_mu(mu) contains as a complete subalgebra an isomorphic copy of the collapse algebra Comp Col(omega_1,mu^{aleph_0}). Consequently, adding a…

We identify a categorical structure of the set of all CFTs. In particular, we show that the set of all CFTs has a natural monoidal strict $2$-category structure with the $1$-morphisms being sequences of deformations and $2$-morphisms…

We study the uniqueness properties of classical semiconjugations for analytic self-maps of the disk, by characterizing them as canonical solutions to certain functional equations. As a corollary, we obtain a complete description of all…

In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.

We prove that coherent configurations can be represented as modules over Frobenius structures in the category of real nonnegative matrices. We generalize the notion of admissible morphism from association schemes to coherent configurations.…

In their seminal paper (Phys. Rev.121, 920 (1961)) Sudarshan, Mathews and Rau investigated properties of the dynamical $A$ and $B$ maps acting on $n$ dimensional quantum systems. Nature of the dynamical maps in open quantum system…

We discuss when the incidence coalgebra of a locally finite preordered set is right co-Frobenius. As a consequence, we obtain that a structural matrix algebra over a field $k$ is Frobenius if and only if it consists, up to a permutation of…

We study compound systems with a classical sector and a quantum sector. Among other consistency conditions we require a canonical structure, that is, a Lie bracket for the dynamical evolution of hybrid observables in the Heisenberg picture,…

We demonstrate that pure C*-algebras form a robust class by proving that pureness follows from very weak comparison and divisibility properties. Using this, we show that every simple, non-elementary C*-algebra with a unique quasitrace and…

The space of monic centered cubic polynomials with marked critical points is isomorphic to C^2. For each n>0, the locus Sn formed by all polynomials with a specified critical point periodic of exact period n forms an affine algebraic set.…

We study differential forms on an algebraic compactification of a moduli space of metric graphs. Canonical examples of such forms are obtained by pulling back invariant differentials along a tropical Torelli map. The invariant differential…

We show that the spectral theorem -- which we understand to be a statement that every self-adjoint matrix admits a certain type of canonical form under unitary similarity -- admits analogues over other $*$-algebras distinct from the complex…

We provide a foundation for working with homological and homotopical methods in categorical algebra. This involves two mutually complementary components, namely (a) the strategic selection of suitable axiomatic frameworks, some well known…

The main motivation for the study of cluster algebras initiated in math.RT/0104151, math.RA/0208229 and math.RT/0305434 was to design an algebraic framework for understanding total positivity and canonical bases in semisimple algebraic…

We study the issue of issue of purity (as a completely positive linear map) for identity maps on operators systems and for their completely isometric embeddings into their C$^*$-envelopes and injective envelopes. Our most general result…

Let $R$ be a commutative ring with unity and $C$ be an $R$-coalgebra. The ring $R$ is clean if every $ r\in R $ is the sum of a unit and an idempotent element of $R$. An $R$-module $M$ is clean if the endomorphism ring of $M$ over $R$ is…

Consider a smooth quasiprojective variety X equipped with a C*-action, and a regular function f: X -> C which is C*-equivariant with respect to a positive weight action on the base. We prove the purity of the mixed Hodge structure and the…