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In the setting of C*-categories, we provide a definition of "spectrum" of a commutative full C*-category as a one-dimensional unital saturated Fell bundle over a suitable groupoid (equivalence relation) and prove a categorical Gelfand…
Each graph and choice of a commutative ring gives rise to an associated graphical group. In this article, we introduce and investigate graph polynomials that enumerate conjugacy classes of graphical groups over finite fields according to…
We introduce two partially overlapping classes of pathwise dualities between interacting particle systems that are based on commutative monoids (semigroups with a neutral element) and semirings, respectively. For interacting particle…
For two countably infinite fields whose multiplicative groups are isomorphic, we examine invariant couplings between the actions that these groups induce on the additive Pontryagin duals of the fields. We show that the actions are disjoint…
We study hyperbolic cohomology classes in the general context of simplicial complexes and prove homological invariance statements for them. We relate the existence of hyperbolic cohomology classes to the non-amenability of the fundamental…
In this paper we consider a two component scalar field theory, with noncommutativity in its conjugate momentum space. We quantize such a theory in a compact space with the help of dressing transformations and we reveal a significant effect…
We define and study homotopy groups of cubical sets. To this end, we give four definitions of homotopy groups of a cubical set, prove that they are equivalent, and further that they agree with their topological analogues via the geometric…
The well known relation between extended supersymmetry and complex geometry in the non-linear sigma-models is reviewed, and some recent developments related to the introduction of the non-anti-commutativity, in the context of the…
Endomorphisms of the measure algebra of commutative hypergroups are investigated. We focus on derivations and higher order derivations which are closely related to moment function sequences of higher rank. We describe the exact connection…
A certain special function of the generalized hypergeometric variety is shown to fulfill a host of useful noncommutative identities.
Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.
A finite quantum hypergroup is a finite-dimensional unital algebra $A$ over the field of complex numbers. There is a coproduct on $A$, a coassociative map from $A$ to $A\otimes A$ assumed to be unital, but it is not required to be an…
If k is an arbitrary field, we construct a category of k-1-motives in which every commutative algebraic k-group G has a dual object $G^{\vee}$. When k is a local field of arbitrary characteristic, we establish Pontryagin duality theorems…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.
We investigate when a computable automorphism of a computable field can be effectively extended to a computable automorphism of its (computable) algebraic closure. We then apply our results and techniques to study effective embeddings of…
The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…
In this paper, we state two combination theorems for relatively quasiconvex subgroups in a relatively hyperbolic group. Applications are given to the separability of double cosets of certain relatively quasiconvex subgroups and the…
The aim of this paper is to give an example of a non-commutative discrete hypergroup associated with $q$-disk polynomials. These are polynomials $R_{l,m}^{(\a)}$ in two non-commuting variables which are expressed through little $q$-Jacobi…
This is an expository plus research paper which mainly exposes preliminary connection and contrast between classical complex dynamics and semigroup dynamics of holomorphic functions. Classically, we expose some existing results of rational…
This (quasi-)survey addresses the quasi-isometry classification of locally compact groups, with an emphasis on amenable hyperbolic locally compact groups. This encompasses the problem of quasi-isometry classification of homogeneous…