Related papers: Interpretation of the Arithmetic in certain groups…

Affine difference algebraic groups are a generalization of affine algebraic groups obtained by replacing algebraic equations with algebraic difference equations. We show that the isomorphism theorems from abstract group theory have…

We perform a comprehensive study of a certain class of discrete symmetries of families of Feynman integrals, defined as affine changes of variables that map different sectors of the family into each other. We show that these transformations…

Fractional supersymmetry denotes a generalisation of supersymmetry which may be constructed using a single real generalised Grassmann variable, $\theta = \bar{\theta}, \, \theta^n = 0$, for arbitrary integer $n = 2, 3, ...$. An explicit…

In this work we use generalized deformed gauge groups for investigation of symmetry of general relativity (GR). GR is formulated in generalized reference frames, which are represented by (anholonomic in general case) affine frame fields.…

Expressions are not functions. Confusing the two concepts or failing to define the function that is computed by an expression weakens the rigour of interval arithmetic. We give such a definition and continue with the required re-statements…

This manuscript represents the author's PhD dissertation thesis.The first part studies decision problems in Thompson's groups F,T,V and some generalizations. The simultaneous conjugacy problem is determined to be solvable for Thompson's…

Let $\pi, \pi'$ be tempered representations of an affine Hecke algebra with positive parameters. We study their Euler--Poincar\'e pairing $EP (\pi,\pi')$, the alternating sum of the dimensions of the Ext-groups. We show that $EP (\pi,\pi')$…

A cuspidal automorphic representation \pi of a group G is said to to be distinguished with respect to a subgroup H if the integral of f along H is nonzero for a cusp form f in the space of \pi. Such period integrals are related to…

This paper considers an invariant of modules over a finite-dimensional Hopf algebra, called the critical group. This generalizes the critical groups of complex finite group representations studied by Benkart, Klivans, Reiner and Gaetz. A…

We implement the Hamiltonian treatment of a nonAbelian noncommutative gauge theory, considering with some detail the algebraic structure of the noncommutative symmetry group. The first class constraints and Hamiltonian are obtained and…

We present a unified ring theoretic approach, based on properties of the Casimir element of a symmetric algebra, to a variety of known divisibility results for the degrees of irreducible representations of semisimple Hopf algebras in…

Let A be the integral closure of the ring of polynomials CC[t], within the field of algebraic functions in one variable. We show that A interprets the ring of integers. This contrasts with the analogue for finite fields, proved to have a…

The affine general linear group acting on a vector space over a prime field is a well-understood mathematical object. Its elementary abelian regular subgroups have recently drawn attention in applied mathematics thanks to their use in…

Let $\Gamma$ be a centerless irreducible higher rank arithmetic lattice in characteristic zero. We prove that if $\Gamma$ is either non-uniform or is uniform of orthogonal type and dimension at least 9, then $\Gamma$ is bi-interpretable…

It is shown that any finitely generated non-elementary Fuchsian group has among its homomorphic images all but finitely many of the alternating groups. This settles in the affirmative a conjecture of Graham Higman.

This text is addressed to mathematicians who are interested in generalized functions and unbounded operators on a Hilbert space. We expose in detail (in a "formal way" - as done by Heisenberg and Pauli - i.e. without mathematical…

This is a survey of several approaches to the framework for working with infinitesimals and infinite numbers, originally developed by Abraham Robinson in the 1960s, and their constructive engagement with the Cantor-Dedekind postulate and…

We define a notion of an arithmetic set in an arbitrary countable group and study properties of these sets in the cases of Abelian groups and non-abelian free groups.

The group algebra of the permutation group is spanned by a set of elements called projectors. The coordinates of permutations expanded in projectors are matrix elements of irreducible representations. The projectors of the permutation group…

This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…