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On the vertex operator algebra associated with rank one lattice we derive a general formula for products of vertex operators in terms of generalized homogeneous symmetric functions. As an application we realize Jack symmetric functions of…
This paper reveals a categorical equivalence connecting two distinct quantum logic structures. The first is the orthomodular lattice, an algebraic system designed to formalize the properties of quantum systems. The second is a finitary…
Real spherical designs and real and complex projective designs have been shown by Delsarte, Goethals, and Seidel to give rise to association schemes when the strength of the design is high compared to its degree as a code. In contrast,…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
The mirror extensions for vertex operator algebras are studied. Two explicit examples which are not simple current extensions of some affine vertex operator algebras of type $A$ are given.
After giving some definitions for vertex operator SUPERalgebras and their modules, we construct an associative algebra corresponding to any vertex operator superalgebra, such that the representations of the vertex operator algebra are in…
We study a class of combinatorial objects that we call "decorated trees". These consist of vertices, arrows and edges, where each edge is decorated by two integers (one near each of its endpoints), each arrow is decorated by an integer, and…
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…
We explore the possibility of extending Mardare et al. quantitative algebras to the structures which naturally emerge from Combinatory Logic and the lambda-calculus. First of all, we show that the framework is indeed applicable to those…
The vertex operator algebras and modules associated to the highest weight modules for the Virasoro algebra over an arbitrary field F whose characteristic is not equal to 2 are studied. The irreducible modules of vertex operator algebra…
In this paper, the notion of unitary vertex operator superalgebra is introduced. It is proved that the vertex operator superalgebras associated to the unitary highest weight representations for the Neveu-Schwarz Lie superalgebra, Heisenberg…
Classical algebraic structures require exact satisfaction of their defining axioms. We propose similarity algebra, a framework extending algebraic and Lie structures to settings where operations satisfy quantitative bounds up to a tolerance…
Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form bigger and more complex ones. Coming historically from algebraic…
In this paper we try to define the higher dimensional analogues of vertex algebras. In other words we define algebras which we hope have the same relation to higher dimensional quantum field theories that vertex algebras have to one…
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 this paper it is shown that the lattice of C*-covers of an operator algebra does not contain enough information to distinguish operator algebras up to completely isometric isomorphism. In addition, four natural equivalences of the…
We study possibilities for algebraic closures, differences between definable and algebraic closures in first-order structures, and variations of these closures with respect to the bounds of cardinalities of definable sets and given sets of…
In this paper, we will study some connections between Hilbert al- gebras and binary block-codes.With these codes, we can eassy obtain orders which determine suplimentary properties on these algebras. We will try to emphasize how, using…
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…
We consider the extension of the Heisenberg vertex operator algebra by all its irreducible modules. We give an elementary construction for the intertwining vertex operators and show that they satisfy a complex parametrized generalized…