dorsal/arxiv
View SchemaLocal systems of twisted vertex operators, vertex operator superalgebras and twisted modules
| Authors | Haisheng Li |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9504022 |
| URL | https://arxiv.org/abs/q-alg/9504022 |
Abstract
We introduce the notion of ``local system of $\Bbb{Z}_{T}$-twisted vertex operators'' on a $\Bbb{Z}_{2}$-graded vector space $M$, generalizing the notion of local system of vertex operators [Li]. First, we prove that any local system of $\Bbb{Z}_{T}$-twisted vertex operators on $M$ has a vertex superalgebra structure with an automorphism $\sigma$ of order $T$ with $M$ as a $\sigma$-twisted module. Then we prove that for a vertex (operator) superalgebra $V$ with an automorphism $\sigma$ of order $T$, giving a $\sigma$-twisted $V$-module $M$ is equivalent to giving a vertex (operator) superalgebra homomorphism from $V$ to some local system of $\Bbb{Z}_{T}$-twisted vertex operators on $M$. As applications, we study the twisted modules for vertex operator (super)algebras associated to some well-known infinite-dimensional Lie (super)algebras and we prove the complete reducibility of $\Bbb{Z}_{T}$-twisted modules for vertex operator algebras associated to standard modules for an affine Lie algebra.
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"abstract": "We introduce the notion of ``local system of $\\Bbb{Z}_{T}$-twisted vertex\noperators\u0027\u0027 on a $\\Bbb{Z}_{2}$-graded vector space $M$, generalizing the notion\nof local system of vertex operators [Li]. First, we prove that any local system\nof $\\Bbb{Z}_{T}$-twisted vertex operators on $M$ has a vertex superalgebra\nstructure with an automorphism $\\sigma$ of order $T$ with $M$ as a\n$\\sigma$-twisted module. Then we prove that for a vertex (operator)\nsuperalgebra $V$ with an automorphism $\\sigma$ of order $T$, giving a\n$\\sigma$-twisted $V$-module $M$ is equivalent to giving a vertex (operator)\nsuperalgebra homomorphism from $V$ to some local system of\n$\\Bbb{Z}_{T}$-twisted vertex operators on $M$. As applications, we study the\ntwisted modules for vertex operator (super)algebras associated to some\nwell-known infinite-dimensional Lie (super)algebras and we prove the complete\nreducibility of $\\Bbb{Z}_{T}$-twisted modules for vertex operator algebras\nassociated to standard modules for an affine Lie algebra.",
"arxiv_id": "q-alg/9504022",
"authors": [
"Haisheng Li"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"title": "Local systems of twisted vertex operators, vertex operator superalgebras and twisted modules",
"url": "https://arxiv.org/abs/q-alg/9504022"
},
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