Related papers: Introduction into Geometry over Division Ring
This is an expository article. We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via…
In various subjects including mathematics, one can hope to use mathematical thinking well when the right kinds of algebraic structure to consider can be discovered or spotted. Therefore, it would help to understand kinds of algebraic…
We introduce the notion of the full quiver of a representation of an algebra, which is a cover of the (classical) quiver, but which captures properties of the representation itself. Gluing of vertices and of arrows enables one to study…
I dedicated the volume $1$ of monograph 'Introduction into Noncommutative Algebra' to studying of algebra over commutative ring. The main topics that I covered in this volume: definition of module and algebra over commutative ring; linear…
By recasting metrical geometry in a purely algebraic setting, both Euclidean and non-Euclidean geometries can be studied over a general field with an arbitrary quadratic form. Both an affine and a projective version of this new theory are…
An algebraic extended bilinear Hilbert semispace is proposed as being the natural representation space for the algebras of von Neumann.This bilinear Hilbert semispace has a well defined structure given by the representation space of an…
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…
This note studies the quantized corner structure of four-dimensional $BF$ theory, classifies the associated free and physical corner algebras and constructs possible representations. In the abelian case, for arbitrary closed oriented…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
A diverse collection of fusion categories may be realized by the representation theory of quantum groups. There is substantial literature where one will find detailed constructions of quantum groups, and proofs of the…
In this pages I give an overview of the relationship between Model Theory, Arithmetic and Algebraic Geometry. The topics will be the basic ones in the area, so this is just an invitation, in the presentation of topics I mainly follow the…
From personal experience, I report about the development of sheaf representations for algebraic structures between the years 1966 and 1976. Starting with rings, lattice-ordered groups and rings it turns to general algebraic structures.
In 2011, a topic containing the concepts of upper and lower periodic subsets of (basic) algebraic structures was introduced and studied. The concept of ``upper periodic subsets'' can be considered as a generalized topic of ideals and…
In these notes, we describe an interesting connection between unitary representations of Lie groups and nets of local algebras, as they appear in Algebraic Quantum Field Theory (AQFT). It is based on first translating the axioms for nets of…
In this paper, we describe the irreducible representations and give a dimension formula for the Framisation of the Temperley-Lieb algebra. We then prove that the Framisation of the Temperley-Lieb algebra is isomorphic to a direct sum of…
For a simple Lie algebra g we consider an analogue of the affine algebra ^gk with n singularities, defined starting from the ring of functions on the n-pointed disk. We study the center of its completed enveloping algebra and prove an…
This is an exposition in order to give an explicit way to understand (1) a non-topological proof for an existence of a base of an affine root system, (2) a Serre-type definition of an elliptic Lie algebra with rank =>2, and (3) the…
We develop basic notions and methods of algebraic geometry over the algebraic objects called hyperrings. Roughly speaking, hyperrings generalize rings in such a way that an addition is `multi-valued'. This paper largely consisits of two…
We investigate the representation theory of certain specializations of the Ariki-Koike algebras, obtained by setting $q=0$ in a suitably normalized version of Shoji's presentation. We classify the simple and projective modules, and describe…
This paper introduces the concept of supermanifolds, viewed as the super-analogues of classical manifolds. Instead of treating supermanifolds as sets of points, we adopt an algebraic-geometric perspective, emphasizing the algebra of…