Related papers: Buildings and classical groups
This is a survey article on the theory of finite complex reflection groups. No proofs are given but numerous references are included.
We introduce a geometric construction which relates to the pentagram map much in the way that a logarithmic spiral relates to a circle. After introducing the construction, we establish some basic geometric facts about it, and speculate on…
Schur rings over the infinite dihedral group $\mathcal{Z}\rtimes\mathcal{Z}_2$ are studied according to properties of Schur rings over infinite groups and the classification of Schur rings over infinite cyclic groups. Schur rings over…
Schur rings are a type of subring of the group ring that is spanned by a partition of the group that meets certain conditions. Past literature has exclusively focused on the finite group case. This paper extends many classic results about…
The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…
Different aspects of application of non-Euclidian geometries in architectural compositions are considered. These aspects are illustrated by examples of Armenian (medieval and contemporary) architectural compositions.
This paper is concerned with rational curves on real classical groups. Our contributions are three-fold: (i) We determine the structure of quadratic rational curves on real classical groups. As a consequence, we completely classify…
This paper is concerned with integrals which integrands are the monomials of matrix elements of irreducible representations of classical groups. Based on analysis on Young tableaux, we discuss some related duality theorems and compute the…
We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.
Groups with a topology that is in consistent one way or another with the algebraic structure are considered. Classical groups with a topology are topological, paratopological, semitopological, and quasitopological groups. We also study…
Here we briefly describe some topics along the lines of projective spaces and related geometric constructions connected to linear algebra, which provide fundamental examples in classical geometry and analysis.
In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic…
We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.
This is a book on Group.
This is a survey paper that also contains some new results. It will appear in the proceedings of the AMS summer research institute on Algebraic Geometry at Santa Cruz.
In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivial examples of rings of new defined…
Generally the study of algebraic deals with the concepts like groups, semigroups, groupoids, loops, rings, near-rings, semirings and vector spaces. The study of bialgebraic structures deals with the study of bistructures like bigroups,…
Many two-dimensional classical field theories have hidden symmetries that form an infinite-dimensional algebra. For those examples that correspond to effective descriptions of compactified superstring theories, the duality group is expected…
It is shown for classical and quantum ensembles that there is a unique quantity which has the properties of a "volume". This quantity is a function of the ensemble entropy, and hence provides a geometric interpretation for the latter. It…
We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…