Related papers: A classical variant of the vertex algebra & the au…
Certain deformable families of vertex algebras acquire at a limit of the deformation parameter a large center, similar to affine Lie algebras at critical level. Then the vertex algebra and its representation category become a bundle over…
A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known…
Practically and intrinsically, inclusions of operator algebras are of fundamental interest. The subject of this paper is intermediate operator algebras of inclusions. There are two previously known theorems which naturally and completely…
We introduce the notion of Leibniz conformal bialgebras, presenting a bialgebra theory for Leibniz conformal algebras as well as the conformal analogues of Leibniz bialgebras. They are equivalently characterized in terms of matched pairs…
Based on the Gerstenhaber Theory, clarification is made of how operadic dynamics may be introduced. Operadic observables satisfy the Gerstenhaber algebra identities and their time evolution is governed by operadic evolution equation. The…
Twisted vertex operators based on rational lattices have had many applications in vertex operator algebra theory and conformal field theory. In this paper, ``relativized'' twisted vertex operators are constructed in a general context based…
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…
Motivated by logarithmic conformal field theory and Gromov-Witten theory, we introduce a notion of a twisted module of a vertex algebra under an arbitrary (not necessarily semisimple) automorphism. Its main feature is that the twisted…
Every four-dimensional ${\cal N}=2$ superconformal field theory comes equipped with an intricate algebraic invariant, the associated vertex operator algebra. The relationships between this invariant and more conventional protected…
We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of…
In this article an interpretation and a proof of some classical \\theorems in analysis on the integration of analytic vectors fields are derived from the algebraic method of realization of bialgebras which are constructed with the data of a…
In the framework of technical analysis for algorithmic trading we use a linear algebra approach in order to define classical technical indicators as bounded operators of the space $l^\infty(\mathbb{N})$. This more abstract view enables us…
In contrast with QFT, classical field theory can be formulated in a strict mathematical way if one defines even classical fields as sections of smooth fiber bundles. Formalism of jet manifolds provides the conventional language of dynamic…
We discuss homogeneous Yang-Baxter deformations of integrable sigma models in terms of twist operators. We show that the twist operators behave as the classical analogue of a Drinfeld twist, for all abelian and almost abelian deformations.…
Thermodynamic equivalence between classical many-body system and some auxiliary nonlinear auxiliary field is proved. Connection between Hamiltonians of the many-body system and the auxiliary field is derived.
In this paper, we study the algebra of twisted vertex operators over an even integral ${\mathbf Z}_2$-lattice, and give a kind of systematic construction of fundamental representations for affine Lie algebras of type $A$, $D$, $E$ with…
Foundations of the theory of vertex algebras are extended to the non-Archimedean setting.
This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, we develop a theory of what we call (weak) quantum vertex $\F((t))$-algebras…
Teleparallel gravity, an empirically equivalent counterpart to General Relativity, represents the influence of gravity using torsional forces. It raises questions about theory interpretation and underdetermination. To better understand the…
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…