Related papers: Cubic algebras and Implication Algebras
In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…
We introduce categories of weak factorization algebras and factorization spaces, and prove that they are equivalent to the categories of ordinary factorization algebras and spaces, respectively. This allows us to define the pullback of a…
In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…
In a recent paper, algebraic descriptions for all non-relativistic spins were derived by elementary means directly from the Lie algebra $\specialorthogonalliealgebra{3}$, and a connection between spin and the geometry of Euclidean…
We show that the binary representation of the integers has a role to play in many aspects of Clifford algebras.
In this article, we only consider finite effect algebras. We define the concepts of classical and quantum effect algebras and show that an effect algebra $E$ is classical if and only if there exists an observable that measures every effect…
We establish a natural correspondence between (the equivalence classes of) cubic solutions of an eiconal type equation and (the isomorphy classes of) cubic Jordan algebras.
This paper develops a geometric model for coupled two-state quantum systems (qubits), which is formulated using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted as entities in the geometric…
Conjunctive table algebras are introduced and axiomatically characterized. A conjunctive table algebra is a variant of SPJR algebra (a weaker form of relational algebra), which corresponds to conjunctive queries with equality. The table…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…
We describe a connection between finite--dimensional representations of quantum affine algebras and affine Hecke algebras.
This is the first of series of talks presented at a permanent Rutgers workshop on noncommutative algebra and geometry. We study here quadratic and quadratic-linear algebras defined by factorizations of noncommutative polynomials and…
Any variety of classical algebras has a so-called conformal counterpart. For example one can consider Lie conformal or associative conformal algebras. Lie conformal algebras are closely related to vertex algebras. We define free objects in…
We introduce the notion of the partial group algebra with projections and relations and show that this C*-algebra is a partial crossed product. Examples of partial group algebras with projections and relations are the Cuntz-Krieger algebras…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e.…
We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other.
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
Theory of representations of F-algebra is a natural development of the theory of F-algebra. Exploring of morphisms of the representation leads to the concepts of generating set and basis of representation. In the book I considered the…