相关论文: OPE-Algebras

This thesis is divided into two parts. The first one is composed of recollections on operad theory, model categories, simplicial homotopy theory, rational homotopy theory, Maurer-Cartan spaces, and deformation theory. The second part deals…

String backgrounds are described as purely geometric objects related to moduli spaces of Riemann surfaces, in the spirit of Segal's definition of a conformal field theory. Relations with conformal field theory, topological field theory and…

We develop a theory of multigraded (i.e., $N^l$-graded) combinatorial Hopf algebras modeled on the theory of graded combinatorial Hopf algebras developed by Aguiar, Bergeron, and Sottile [Compos. Math. 142 (2006), 1--30]. In particular we…

We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product…

We introduce the notion of a conformal design based on a vertex operator algebra. This notation is a natural analog of the notion of block designs or spherical designs when the elements of the design are based on self-orthogonal binary…

Pseudo $MV$-algebras are a non-commutative generalization of $MV$-algebras. The main purpose of the paper is to introduce and investigate orthocomplete pseudo $MV$-algebras. We use the concepts of projectable pseudo $MV$-algebras and large…

In this paper, we construct the fundamental theorem of UP-homomorphisms in UP-algebras. We also give an application of the theorem to the first, second, third and fourth UP-isomorphism theorems in UP-algebras.

The notion of Lie algebroids over a topological ringed space provides a unified framework to study various geometric structures. This geometric concept is intimately connected with well-known algebraic structures, including Gerstenhaber…

We introduce a generalization of the notion of a Koszul algebra, which includes graded algebras with relations in different degrees, and we establish some of the basic properties of these algebras. This class is closed under twists, twisted…

One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra [K]. A Lie pseudoalgebra is a generalization of the…

It is shown that a certain representation of the Heisenberg type Krichever-Novikov algebra gives rise to a state field correspondence that is quite similar to the vertex algebra structure of the usual Heisenberg algebra. Finally a…

We develop and exposit some general algebra useful for working with certain algebraic structures that arise in stable homotopy theory, such as those encoding well-behaved theories of power operations for $\mathbb{E}_\infty$ ring spectra. In…

Conformal algebras, recently introduced by Kac, encode an axiomatic description of the singular part of the operator product expansion in conformal field theory. The objective of this paper is to develop the theory of ``multi-dimensional''…

In this paper we prove that, in the category of chain complexes, partial algebras can be functorially replaced by quasi-isomorphic algebras. In particular, partial algebras contain all of the important homological and homotopical…

In this paper we introduce arrow algebras, simple algebraic structures which induce elementary toposes through the tripos-to-topos construction. This includes localic toposes as well as various realizability toposes, in particular, those…

We present a realisation of the universal/simple Bershadsky--Polyakov vertex algebras as subalgebras of the tensor product of the universal/simple Zamolodchikov vertex algebras and an isotropic lattice vertex algebra. This generalises the…

Various concepts associated with quadratic algebras admit natural generalizations when the quadratic algebras are replaced by graded algebras which are finitely generated in degree 1 with homogeneous relations of degree N. Such algebras are…

These are the lecture notes for a course taught at Tsinghua University in the spring of 2022. In these notes, we develop the basic theory of vertex operator algebras (VOAs) and their conformal blocks using complex-analytic methods. In…

The fundamental ingredients that build the observables in conformal field theory are the spectrum of operators and the OPE coefficients, or equivalently, the two- and three-point functions of the theory. Recently an inversion formula…

In this paper, we describe a general theory of modules over an algebra over an operad. We also study functors between categories of modules. Specializing to the operad E_d of little d-dimensional disks, we show that each (d-1)-manifold…