Related papers: The structure of reversing symmetry groups
We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.
The m-weak group inverse was recently studied in the literature. The purpose of this paper is to investigate new properties of this generalized inverse for ring elements. We introduce the m-weak group decomposition for a ring element and…
A simple observation, showing that every groupoid becomes an inverse semigroup after adding one element. In such inverse semigroups all idempotents are mutually orthogonal. This fact implies that every C*-algebra of a discrete groupoid is a…
Various aspects of Supersymmetry in 1-dimensional systems are analyzed.
The problem of homological stability helps us to catch the structure of group homology. We calculate homological stability of special orthogonal groups, and we also calculate the stability of orthogonal groups with determinant-twisted…
Using small cancellation for rotating families of groups, we construct new examples of aspherical polyhedra.
We describe geometric non-commutative formal groups in terms of a geometric commutative formal group with a Poisson structure on its splay algebra. We describe certain natural properties of such Poisson structures and show that any such…
We take the first step toward a structure theory that includes both operations of a ring $\mathcal{R}$. More precisely, we prove a series of inverse results for the structure of sets $A\subseteq \mathbf{F}_p$ such that, under certain…
We describe the structure of the algebraic group of automorphisms of all simple finite dimensional Lie superalgebras. Using this and \'etale cohomology considerations, we list all different isomorphism classes of the corresponding twisted…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
A binary operation on any set induces a binary operation on its subsets. We explore families of subsets of a group that become a group under the induced operation and refer to such families as power groups of the given group. Our results…
Toral automorphisms, represented by unimodular integer matrices, are investigated with respect to their symmetries and reversing symmetries. We characterize the symmetry groups of GL(n,Z) matrices with simple spectrum through their…
Symmetry techniques based on group theory play a prominent role in the analysis of nuclear phenomena, and in particular in the understanding of observed regular patterns in nuclear spectra and selection rules for electromagnetic…
There are many Lie groups used in physics, including the Lorentz group of special relativity, the spin groups (relativistic and non-relativistic) and the gauge groups of quantum electrodynamics and the weak and strong nuclear forces.…
We give a number of constructions where inverse limits seriously degrade properties of regular rings, such as unit-regularity, diagonalisation of matrices, and finite stable rank. This raises the possibility of using inverse limits to…
We consider the basic features of complex dynamic and control systems, including systems having hierarchical structure. Special attention is paid to the problems of design and synthesis of complex systems and control models, and to the…
Group Theory techniques can aid greatly the determination of magnetic structures. The integration of their calculations into new and existing refinement programs is an ongoing development that will simplify and make more rigorous the…
In the statistical description of dynamical systems, an indication of the irreversibility of a given state change is given geometrically by means of a (pre-)ordering of state pairs. Reversible state changes of classical and quantum systems…
Lie-symmetry methods are used to determine the symmetry group of reduced magnetohydrodynamics. This group allows for arbitrary, continuous transformations of the fields themselves, along with space-time transformations. The derivation…
For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.