Related papers: Matricial Closure
We reconsider the quantum inverse scattering approach to the one-dimensional Hubbard model and work out some of its basic features so far omitted in the literature. It is our aim to show that $R$-matrix and monodromy matrix of the Hubbard…
Associating to each pre-order on the indices 1,...,n the corresponding structural matrix ring, or incidence algebra, embeds the lattice of n-element pre-orders into the lattice of n x n matrix rings. Rings within the order-convex hull of…
In this note, a condition (\emph{open persistence}) is presented under which a (pre)closure operation on submodules (resp. ideals) over rings of global sections over a scheme $X$ can be extended to a (pre)closure operation on sheaves of…
We describe a closed operator functional calculus in Banach modules over the group algebra $L^1(\mathbb R)$ and illustrate its usefulness with a few applications. In particular, we deduce a spectral mapping theorem for operators in the…
The one-dimensional transverse field Ising model is solved by continuous unitary transformations in the high-field limit. A high accuracy is reached due to the closure of the relevant algebra of operators which we call string operators. The…
In this paper we investigate a categorical aspect of $n$-trivial extension of a ring by a family of modules. Namely, we introduce the right (resp., left) $n$-trivial extension of a category by a family of endofunctors. Among other results,…
This book is a rigorous and conceptually oriented introduction to ring theory. The emphasis is on structural understanding rather than encyclopedic coverage: rings are studied through ideals, homomorphisms, quotients, and universal…
This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving…
We derive one-point functions of the loop operators of Hermitian matrix-chain models at finite $N$ in terms of differential operators acting on the partition functions. The differential operators are completely determined by recursion…
I present a derivation of form factors in the Algebraic Cluster Model for an arbitrary number of identical clusters. The form factors correspond to representation matrix elements which are derived in closed form for the harmonic oscillator…
We consider a class of block operator matrices arising in the study of scattering passive systems, especially in the context of boundary control problems. We prove that these block operator matrices are indeed a subclass of block operator…
Modular invariance is a necessary condition for the consistency of any closed string theory. In particular, it imposes stringent constraints on the spectrum of orbifold theories, and in principle determines their spectrum uniquely up to…
We study the dynamics of a finite chain of diffusively coupled Lorenz oscillators with periodic boundary conditions. Such rings possess infinitely many fixed states, some of which are observed to be stable. It is shown that there exists a…
The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the…
We consider the problem of characterizing entrywise functions that preserve the cone of positive definite matrices when applied to every off-diagonal element. Our results extend theorems of Schoenberg [Duke Math. J. 9], Rudin [Duke Math. J.…
This paper is concerned with the taxonomy of finitely complete categories, based on 'matrix properties' - these are a particular type of exactness properties that can be represented by integer matrices. In particular, the main result of the…
General approach to the multiplication or adjoint operation of $2\times 2$ block operator matrices with unbounded entries are founded. Furthermore, criteria for self-adjointness of block operator matrices based on their entry operators are…
Let $G$ be a group acting via ring automorphisms on an integral domain $R.$ A ring-theoretic property of $R$ is said to be $G$-invariant, if $R^G$ also has the property, where $R^G=\{r\in R \ | \ \sigma(r)=r \ \text{for all} \ \sigma\in…
We derive a closed formula for the matrix elements of the volume operator for canonical Lorentzian quantum gravity in four spacetime dimensions in the continuum in a spin-network basis. We also display a new technique of regularization…
This paper is devoted to the spectral properties of a class of unitary operators with a matrix representation displaying a band structure. Such band matrices appear as monodromy operators in the study of certain quantum dynamical systems.…