Related papers: Effective equivalence relations and principal quan…
Transformation properties of a class of generalized Kawahara equations with time-dependent coefficients are studied. We construct the equivalence groupoid of the class and prove that this class is not normalized but can be presented as a…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
We introduce the notion of the power quandle of a group, an algebraic structure that forgets the multiplication but keeps the conjugation and the power maps. Compared with plain quandles, power quandles are much better invariants of groups.…
Inspired by the theory of apartness relations of Scott, we establish a positive theory of dissimilarity valued in an involutive quantale $\mathsf{Q}$ without the aid of negation. It is demonstrated that a set equipped with a…
A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…
Based on the properties of the poset of those equivalence relations of a multialgebra for which the factor multialgebra is a universal algebra, we give a characterization for the fundamental relations of a multialgebra. We point out the…
In this paper subcentral (resp., central) idempotent series and composition subcentral (resp., central) idempotent series in an inverse semigroup are introduced and investigated. It is shown that if $S=EG$ is a factorizable inverse monoids…
We develop a semigroup approach to representation theory for pro-Lie groups satisfying suitable amenability conditions. As an application of our approach, we establish a one-to-one correspondence between equivalence classes of unitary…
This paper extends the fundamental results of frame theory to a non-commutative setting where the role of locales is taken over by \'etale localic categories. This involves ideas from quantale theory and from semigroup theory, specifically…
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.
We introduce an equivariant version of contextuality with respect to a symmetry group, which comes with natural applications to quantum theory. In the equivariant setting, we construct cohomology classes that can detect contextuality. This…
Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was…
The renormalization-group improved effective potential ---to leading-log and in the linear curvature approximation--- is constructed for ``finite'' theories in curved spacetime. It is not trivial and displays a quite interesting,…
Lie groups and quantum algebras are connected through their common universal enveloping algebra. The adjoint action of Lie group on its algebra is naturally extended to related q-algebra and q-coalgebra. In such a way, quantum structure can…
The most developed aspect of the theory of finite semigroups is their classification in pseudovarieties. The main motivation for investigating such entities comes from their connection with the classification of regular languages via…
A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a ring and a semiring -- a semiring whose additive monoid is…
We introduce a class of strongly \'{e}tale difference algebras, whose role in the study of difference equations is analogous to the role of \'{e}tale algebras in the study of algebraic equations. We deduce an improved version of Babbitt's…
We introduce locally involutive semigroups and embed them into the category of ordered groupoids. This embedding restricts to a correspondence between quasi-involutive semigroups and ordered groupoids with mediator, extending the classical…
In orthodox Standard Quantum Mechanics (SQM) bases and factorizations are considered to define quantum states and entanglement in relativistic terms. While the choice of a basis (interpreted as a measurement context) defines a state…