Simple Conformal Algebras Generated by Jordan Algebras

Simple Jordan conformal superalgebras

We classify simple finite Jordan conformal superalgebras and establish preliminary results for the classification of simple finite Jordan pseudoalgebras.

On Correlation Functions of Vertex Operator Algebras Associated to Jordan Algebras

In this paper we study certain vertex operator algebras associated to Jordan algebras and compute the correlation function of basic fields

On VOAs Associated to Jordan Algebras of Type $C$

In this article, we construct certain universal VOAs whose Greiss algebras are type C Jordan algebras. We also prove the corresponding simplicity result.

Deformation of central charges, vertex operator algebras whose Griess algebras are Jordan algebras

If a vertex operator algebra $V=\oplus_{n=0}^{\infty}V_n$ satisfies $\dim V_0=1, V_1=0$, then $V_2$ has a commutative (nonassociative) algebra structure called Griess algebra. One of the typical examples of commutative (nonassociative) algebras is a Jordan algebra. For example, the set $Sym_d(\C)$ of symmetric matrices of degree $d$ becomes a Jordan algebra. On the other hand, in the theory of vertex operator algebras, central charges influence the properties of vertex operator algebras. In this paper, we construct vertex operator algebras with central charge $c$ and its Griess algebra is isom…

Jacobi-Jordan 共形代数：基础、构造及相关结构

Jacobi-Jordan conformal algebras: Basics, Constructions and related structures

本文引入并研究了 Jacobi-Jordan conformal algebra 的概念，探讨了其共形模、表示、O-算子、共形导子、二次结构及统一积，并通过构造上同调对象为 C[delta]-split extending structures problem 提供了理论解答。

The Tits--Kantor--Koecher construction for Jordan dialgebras

We study a noncommutative generalization of Jordan algebras called Jordan dialgebras. These are algebras that satisfy the identities $[x_1 x_2]x_3= 0$, $(x_1^2,x_2,x_3)=2(x_1,x_2,x_1x_3)$, $x_1(x_1^2 x_2)=x_1^2(x_1 x_2)$; they are related with Jordan algebras in the same way as Leibniz algebras are related to Lie algebras. We present an analogue of the Tits---Kantor---Koecher construction for Jordan dialgebras that provides an embedding of such an algebra into Leibniz algebra.