Related papers: Effective equivalence relations and principal quan…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…
We define notions of generically and coarsely computable relations and structures and functions between structures. We investigate the existence and uniqueness of equivalence structures in the context of these definitions
We extend the classical notion of standardly stratified $k$-algebra (stated for finite dimensional $k$-algebras) to the more general class of rings, possibly without $1,$ with enough idempotents. We show that many of the fundamental…
The quantum lens spaces form a natural and well-studied class of noncommutative spaces which can be subjected to classification using algebraic invariants by drawing on the fully developed classification theory of unital graph…
Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased…
In this work, the notion of a quantum inverse semigroup is introduced as a linearized generalization of inverse semigroups. Beyond the algebra of an inverse semigroup, which is the natural example of a quantum inverse semigroup, several…
We prove a generalisation of the correspondence, due to Resende and Lawson--Lenz, between \'etale groupoids---which are topological groupoids whose source map is a local homeomorphisms---and complete pseudogroups---which are inverse monoids…
We introduce the notion of groupoid pre-equivalences and prove that they give rise to groupoid equivalences by taking certain quotients. Then, given an equivalence of Fell bundles $\mathscr{B}$ and $\mathscr{C}$ and another equivalence…
** The primary topic of this dissertation is the study of the relationships between parts and wholes as described by particular physical theories, namely generalized probability theories in a quasi-classical physics framework and…
Boolean spaces with internal semigroups generalize profinite semigroups and are pertinent for the recognition of not-necessarily regular languages. Via recognition, the study of existential quantification in logic on words amounts to the…
In the framework of Category Theory, we study the association between finite--dimensional representations of a compact quantum group and quantum vector bundles with linear connections for a given quantum principal bundle with a principal…
We construct quantized versions of generic bases in quantum cluster algebras of finite and affine types. Under the specialization of $q$ and coefficients to 1, these bases are generic bases of finite and affine cluster algebras.
The longstanding issue of general covariance in effective models of quantum gravity is addressed, which arises when canonical quantum gravity leads to a semiclassical model described by an effective Hamiltonian constraint. In the context of…
We introduce the concept of a Girard couple, which consists of two (not necessarily unital) quantales linked by a strong form of duality. The two basic examples of Girard couples arise in the study of endomorphism quantales and of the…
We construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. As all previously known examples, our examples are contracted semigroup algebras and the underlying…
Semiuniform semigroups provide a natural setting for the convolution of generalized finite measures on semigroups. A semiuniform semigroup is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the…
The notion of a categorical quotient can be generalized since its standard categorical concept does not recover the expected quotients in certain categories. We present a more general formulation in the form of $\mathcal{F}$-quotients in a…
Self-similar potentials generalize the concept of shape-invariance which was originally introduced to explore exactly-solvable potentials in quantum mechanics. In this article it is shown that previously introduced algebraic approach to the…
Let $A$ be a unital separable \CA and $B=C\otimes {\cal K},$ where $C$ is a unital \CA. Let $\tau: A\to M(B)/B$ be a weakly unital full essential extensions of $A$ by $B.$ We show that there is a bijection between a quotient group of…