Related papers: Isotopic pairs and their representations. II. A ge…
We introduce the concept of a Girard couple, which consists of two (not necessarily unital) quantales linked by a strong form of duality. The two basic examples of Girard couples arise in the study of endomorphism quantales and of the…
This review presents an overview of various kinds of models -- physical, abstract, mathematical, visual -- that can be used to present the concepts and applications of Einstein's general theory of relativity at the level of undergraduate…
The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.
An algebraic isopair is a commuting pair of pure isometries that is annihilated by a polynomial defining a distinguished variety $\mathcal{V}$. The notion of the rank of a pure algebraic isopair with finite bimultiplicity is introduced. For…
The notion of quantum matrix pairs is defined. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of…
The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on smooth partitions of unity and tangent…
A representation theory for Bol algebras is proposed. For a suitable (2,3)-cohomology theory for Bol algebras, we define a (2,3)-coboundary with companion and next we define a (2,3)-cohomology group. Deformations of Bol algebras are…
This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it is understood by mathematicians. The…
Dual representations $V$ and $V^*$ of a complex connected algebraic group $G$ simultaneously have either infinitely or finitely many orbits. Whenever the latter holds, the orbits in $V$ and $V^*$ are in a bijective correspondence called…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
We analyze the abstract representations of the groups of rational points of even-dimensional quasi-split special unitary groups associated with quadratic field extensions. We show that, under certain assumptions, such representations have a…
We study general aspects of the reductive dual pair correspondence, also known as Howe duality. We make an explicit and systematic treatment, where we first derive the oscillator realizations of all irreducible dual pairs: $(GL(M,\mathbb…
In this note we introduce generalised pairs from the perspective of the evolution of the notion of space in birational algebraic geometry. We describe some applications of generalised pairs in recent years and then mention a few open…
In this paper, we give a purely cohomological interpretation of the extension problem for associative algebras; that is the problem of extending an associative algebra by another associative algebra. We then give a similar interpretation of…
Understanding the structure of a graph along with the structure of its subgraphs is important for several problems in graph theory. Two examples are the Reconstruction Conjecture and isomorph-free generation. This paper raises the question…
We study the representation dimension of the class of algebras known as quantum complete intersections. For such an algebra, we show that the representation dimension is at most twice its codimension. Moreover, we show that the…
We establish representation types (finite, tame or wild) of finite dimensional Munn algebras with semisimple bases. As an application, we establish representation types of finite 0-simple semigroups and their mutually annihilating unions.
We begin by reviewing the definition of 3-Lie algebras and the fundamental concepts of matched pairs. Subsequently, we introduce the representation theory of matched pairs and define the semidirect product. Building on this foundation, we…
The purpose of this article is to study certain binary relations of endomorphisms over infinite dimensional vector spaces defined by GD1 and 1GD generalized inverses. In order to do so, these generalized inverses are studied over arbitrary…
Let $E$ be an elliptic curve with complex multiplication by a ring $R$, where $R$ is an order in an imaginary quadratic field or quaternion algebra. We define sesquilinear pairings ($R$-linear in one variable and $R$-conjugate linear in the…