Related papers: Some finite properties for vertex operator superal…

Odd, positive-definite, integral, unimodular lattices N of rank 24 were classified by Borcherds. There are 273 isometry classes of such lattices. Associated to them are vertex superalgebras $V_N$ of central charge c=24. We show that at…

Let V be a simple vertex operator algebra satisfying the following conditions: (i) The homogeneous subspaces of V of weights less than 0 are 0, the homogeneous subspace of V of weight 0 is spanned by the vacuum and V' is isomorphic to V as…

We define vertex cover algebras for weighted simplicial multicomplexes and prove basics properties of them. Also, we describe these algebras for multicomplexes which have only one maximal facet and we prove that they are finitely generated.

This paper may be viewed as having two aims. First, we continue our study of algebras of operators on a Hilbert space which have a contractive approximate identity, this time from a more Banach algebraic point of view. Namely, we mainly…

In this paper, we study Rota-Baxter operators and super $\mathcal{O}$-operator of associative superalgebras, Lie superalgebras, pre-Lie superalgebras and $L$-dendriform superalgebras. Then we give some properties of pre-Lie superalgebras…

We demonstrate that, for CFT vertex operator algebras, C_2-cofiniteness and rationality is equivalent to regularity. In addition, we show that, for C_2-cofinite vertex operators algebras, irreducible weak modules are ordinary modules and…

We construct an iterative procedure to compute the vertex operators of the closed superstring in the covariant formalism given a solution of IIA/IIB supergravity. The manifest supersymmetry allows us to construct vertex operators for any…

In this article, we describe the trace formulae of composition of several (up to four) adjoint actions of elements of the Lie algebra of a vertex operator algebra by using the Casimir elements. As an application, we give constraints on the…

We consider two different methods of associating vertex algebraic structures with the level $1$ principal subspaces for $U_q (\widehat{\mathfrak{sl}}_2)$. In the first approach, we introduce certain commutative operators and study the…

All operator algebras have (not necessarily irreducible) boundary representations. A unital operator algebra has enough such boundary representations to generate its C*-envelope.

In this article, using an idea of the physics superselection principal, we study a modularity on vertex operator algebras arising from semisimple primary vectors. We generalizes the theta functions on vertex operator algebras and prove that…

The algebraic structure on the subspace of the quasi-primary vectors given by the projection of the (n) products of a conformal superalgebra is formulated. As an application the complete list of simple physical conformal superalgebras is…

The purpose of this paper is to study pseudo-Euclidean and symplectic Hom-alternative superalgebras and discuss some of their proprieties and provide construction procedures. We also introduce the notion of Rota-Baxter operators of…

Let $P(N,V)$ denote the vector space of polynomials of maximal degree less than or equal to $N$ in $V$ independent variables. This space is preserved by the enveloping algebra generated by a set of linear, differential operators…

A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…

This article is a continuation of our work on the classification of holomorphic framed vertex operator algebras of central charge 24. We show that a holomorphic framed VOA of central charge 24 is uniquely determined by the Lie algebra…

Using the pure spinor formalism for the superstring in an $AdS_5\times S^5$ background, a simple expression is found for half-BPS vertex operators. At large radius, these vertex operators reduce to the usual supergravity vertex operators in…

Let V be a simple vertex operator algebra and let G be a finite automorphism group of V. In [DY], it was shown that any irreducible V-module is a completely reducible V^G-module where V^G is the G-invariant sub-vertex operator algebra of V.…

We first establish some general results connecting real and complex Lie algebras of first-order differential operators. These are applied to completely classify all finite-dimensional real Lie algebras of first-order differential operators…

Motivated by the theory of unitary representations of finite dimensional Lie supergroups, we describe those Lie superalgebras which have a faithful finite dimensional unitary representation. We call these Lie superalgebras unitary. This is…