Bimodules associated to vertex operator algebras

Trans. Amer. Math. Soc.

2008

Self Cite

Abstract. This paper studies the twisted representations of vertex operator algebras. Let V be a vertex operator algebra and g an automorphism of V of finite order T. For any m, n ∈The collection of these bimodules determines any admissible g-twisted V -module completely. A Verma type admissible g-twisted V -module is constructed naturally from any A g,m (V )-module. Furthermore, it is shown with the help of bimodule theory that a simple vertex operator algebra V is g-rational if and only if its twisted associative algebra A g (V ) is semisimple and each irreducible admissible g-twisted V -module is ordinary.

“…If g = 1, the A g,n,m (V ) = A n,m (V ) has been defined and studied in [DJ1]. We have the first main theorem in this paper.…”

Section: Chongying Dong and Cuipo Jiangmentioning

confidence: 76%

“…where we have used Proposition 5.1 of [DJ1] and Lemma 3.4 in the last two steps. Next, we prove that…”

Section: Proof Letmentioning

confidence: 99%

“…This section is an extension of bimodule theory developed in [DJ1] from the untwisted case to the twisted case. In particular we will construct…”

Section: Definition 21 a Weak G-twisted V -Module M Is A Vector Spamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bimodules and $g$-rationality of vertex operator algebras

Dong

Trans. Amer. Math. Soc.

2008

Self Cite

“…For homo-geneous u ∈ V , define o n,m (u) : M (m) → M (n) by o n,m (u)w = u wtu+m−n−1 w, (6.1) where w ∈ M (m) and u wtu+m−n−1 is the component operator of Y M (u, z) = n∈Z u n z −n−1 .Note that i 1 − i 2 = r then o n,m (u)w = 0. As in[18], the following lemma gives the representation theory reason for Proposition 5.4.Lemma 6.1. We have o n,m (a) = 0 on M (m) for all a ∈ O n,m (V ).…”

mentioning

confidence: 95%

Bimodules associated to vertex operator superalgebras

Wei

Sci. China Ser. A-Math.

2008

Let V be a vertex operator superalgebra and m, n ∈ 1 2 Z+. We construct an An(V ) − Am(V )-bimodule An,m(V ) which characterizes the action of V from the level m subspace to level n subspace of an admissible V -module. We also construct the Verma type admissible V -module from an Am(V )-module by using bimodules Keywords: vertex operator algebra, admissible module, vertex operator superalgebra, associative algebra, bimodule MSC(2000): 17B69

Bimodule and twisted representation of vertex operator algebras

Jiao

2015

Sci. China Math.

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 $\AA_{g,n}(M)$ and study its some properties, discuss the connections between bimodule $\AA_{g,n}(M)$ and intertwining operators. Especially, bimodule $\AA_{g,n-\frac{1}{T}}(M)$ is a natural quotient of $\AA_{g,n}(M)$ and there is a linear isomorphism between the space ${\cal I}_{M\,M^j}^{M^k}$ of intertwining operators and the space of homomorphisms $\rm{Hom}_{A_{g,n}(V)}(\AA_{g,n}(M)\otimes_{A_{g,n}(V)}M^j(s), M^k(t))$ for $s,t\leq n, M^j, M^k$ are $g$-twisted $V$ modules, if $V$ is $g$-rational