Related papers: Twisted vertex operators and Bernoulli polynomials

Using $n$ finite order automorphisms on a simple complex Lie algebra we construct twisted $n$-toroidal Lie algebras. Thus obtaining Lie algebras wich have a rootspace decomposition. For the case $n=2$ we list certain simple Lie algebras and…

In this article, we develop a general technique for proving the uniqueness of holomorphic vertex operator algebras based on the orbifold construction and its "reverse" process. As an application, we prove that the structure of a strongly…

Twisted modules for N=2 supersymmetric vertex operator superalgebras are classified for the vertex operator superalgebra automorphisms which are lifts of a finite automorphism of the N=2 Neveu-Schwarz Lie superalgebra representation. These…

A vertex algebra with an action of a group $G$ comes with a notion of $g$-twisted modules, forming a $G$-crossed braided tensor category. For a Lie group $G$, one might instead wish for a notion of $(\mathrm{d}+A)$-twisted modules for any…

We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers of vertex operator algebras which are…

We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are ``open-string-theoretic,'' ``noncommutative'' generalizations of the notions of vertex algebra and of…

We prove the first nontrivial reconstruction theorem for modular tensor categories: the category associated to any twisted Drinfeld double of any finite group, can be realised as the representation category of a completely rational…

In this paper, we construct a large class of new simple modules over the twisted $N=2$ superconformal algebra. These new simple modules are restricted modules based on the simple modules over certain finite-dimensional solvable Lie…

Let $V$ be a strongly rational vertex operator algebra, and let $g_1, g_2, g_3$ be three commuting finitely ordered automorphisms of $V$ such that $g_1g_2=g_3$ and $g_i^T=1$ for $i=1, 2, 3$ and $T\in \N$. Suppose $M^1$ is a $g_1$-twisted…

A twisting system is one of the major tools to study graded algebras, however, it is often difficult to construct a (non-algebraic) twisting system if a graded algebra is given by generators and relations. In this paper, we show that a…

This paper, together with Part II, expands the results of math.DG/9803051. In Part I we study the twisted index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective…

In this paper we apply the twisted Alexander polynomial to study the fibering and genus detecting problems for oriented links. In particular we generalize a conjecture of Dunfield, Friedl and Jackson on the torsion polynomial of hyperbolic…

The present article takes advantage of the properties of algebras in the category of S-modules (twisted algebras) to investigate further the fine algebraic structure of Hopf operads. We prove that any Hopf operad P carries naturally the…

We construct new families of discrete vector orthogonal polynomials that have the property to be eigenfunctions of some difference operator. They are extensions of Charlier, Meixner and Kravchuk polynomial systems. The ideas behind our…

We construct a braided structure on the algebra of K\"ahler differential forms of a commutative algebra twisted by an endomorphism. This generalises the construction done in M. Karoubi, Quantum Methods in Algebraic Topology, see…

In this paper, we study the perturbative aspects of a twisted version of the two-dimensional $(0,2)$ heterotic sigma model on a holomorphic gauge bundle $\mathcal E$ over a complex, hermitian manifold $X$. We show that the model can be…

In this paper, for a vertex operator algebra $V$ with an automorphism $g$ of order $T,$ an admissible $V$-module $M$ and a fixed nonnegative rational number $n\in\frac{1}{T}\Bbb{Z}_{+},$ we construct an $A_{g,n}(V)$-bimodule $\AA_{g,n}(M)$…

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…

Let X be a smooth algebraic variety over a field K containing the real numbers. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf of X. These are stack-like versions of usual deformations. We…

The aim of this work is to investigate the structure of some skew twisted algebras, when the coefficient ring is a localization of the polynomial ring over the field of characteristic zero, and an involution is provided. A parallel…