相关论文: Alg\`ebre absolue
We introduce a new approach that allows us to determine the structure of Zhu's algebra for certain vertex operator (super)algebras which admit horizontal $\mathbb{Z} $-grading. By using this method and an earlier description of Zhu's…
Working in the axiomatic framework recently proposed by Gaberdiel and Goddard, we prove a generalized version of Zhu's Theorem; for any chiral bosonic conformal field theory on the sphere, our result characterizes the chiral blocks in terms…
We prove that higher level Zhu algebras of a vertex operator algebra are isomorphic to subquotients of its universal enveloping algebra.
A comprehensive introduction to logarithmic conformal field theory, using an algebraic point of view, is given. A number of examples are explained in detail, including the c=-2 triplet theory and the k=-4/3 affine su(2) theory. We also give…
Modulo the ideal generated by the derivative fields, the normal ordered product of holomorphic fields in two-dimensional conformal field theory yields a commutative and associative algebra. The zero mode algebra can be regarded as a…
Let F be a function field in two variables over an algebraically closed field of characteristic zero. The main part of this Bourbaki talk describes A. J. de Jong's proof (Duke Math. J. 123 (2004) 71-94) that index and exponent coincide for…
It is proved that Zhu's algebra for vertex operator algebra associated to a positive-definite even lattice of rank one is a finite-dimensional semiprimitive quotient algebra of certain associative algebra introduced by Smith. Zhu's algebra…
Through the introduction of new ideals, and with the assistance of the $d$-th mode transition algebras $\mathfrak{A}_d$, for $d\in \mathbb{N}$, we show how Zhu's associative algebra $\mathsf{A}$, conventionally valued for tracking…
We prove an analogue of the prime number theorem for finite fields.
The purpose of this note is to demonstrate the advantages of Y.-Z.~Huang's definition of the Zhu algebra (Comm.\ Contemp.\ Math., 7 (2005), no.~5, 649--706) for an arbitrary vertex algebra, not necessarily equipped with a Hamiltonian…
We show the equivalence between Deitmar's and Toen-Vaquie's notions of schemes over F_1 (the 'field with one element'), establishing a symmetry with the classical case of schemes, seen either as spaces with a structure sheaf, or functors of…
Let $K$ be a function field of one variable over a finite field $\mathbb{F}$. Weil's celebrated theorem states that the congruent zeta function of $K/\mathbb{F}$ is determined by the $\mathrm{Gal}(\overline{\mathbb{F}}/\mathbb{F})$-module…
We consider various homotopy algebras related to Yang-Mills theory and two-dimensional conformal field theory (CFT). Our main objects of study are Yang-Mills $L_{\infty}$ and $C_{\infty}$ algebras and their relation to the certain algebraic…
Conformal algebra is an axiomatic description of the operator product expansion (or rather its Fourier transform) of chiral fields in a conformal field theory. This is a review of recent developments in the subject.
In Section 1 we review various equivalent definitions of a vertex algebra V. The main novelty here is the definition in terms of an indefinite integral of the lambda-bracket. In Section 2 we construct, in the most general framework, the Zhu…
I show by the example of the general linear group, how one can deduce from my previous work "Decomposition spectrale d'un groupe reductif $p$-adique" (to appear in Journal of the Institute of Mathematics of Jussieu) precise information on…
We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…
We develop a theory of perfect algebraic spaces that extend the so-called perfect schemes to the setting of algebraic spaces. We prove several desired properties of perfect algebraic spaces. This extends some previous results of perfect…
A new rigorous approach to conformal field theory is presented. The basic objects are families of complex-valued amplitudes, which define a meromorphic conformal field theory (or chiral algebra) and which lead naturally to the definition of…
We investigate associative quotients of vertex algebras. We also give a short construction of the Zhu algebra, and a proof of its associativity using elliptic functions.