On the unitary structures of vertex operator superalgebras
| Autor: | Xingjun Lin, Chunrui Ai |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Vertex (graph theory)
Pure mathematics Algebra and Number Theory Mathematics::Operator Algebras Direct sum Mathematics::Rings and Algebras 010102 general mathematics Lie superalgebra Positive-definite matrix 01 natural sciences Unitary state Linear subspace Superalgebra Vertex operator algebra Computer Science::Discrete Mathematics Mathematics::Quantum Algebra Mathematics - Quantum Algebra 0103 physical sciences FOS: Mathematics Quantum Algebra (math.QA) 010307 mathematical physics 0101 mathematics Mathematics::Representation Theory Mathematics |
| Zdroj: | Journal of Algebra. 487:217-243 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2017.05.030 |
| Popis: | In this paper, the notion of unitary vertex operator superalgebra is introduced. It is proved that the vertex operator superalgebras associated to the unitary highest weight representations for the Neveu-Schwarz Lie superalgebra, Heisenberg superalgebras and to positive definite integral lattices are unitary vertex operator superalgebras. The unitary structures are then used to study the structures of vertex operator superalgebras, it is proved that any unitary vertex operator superalgebra is a direct sum of strong CFT type unitary simple vertex operator superalgebras. The classification of unitary vertex operator superalgebras generated by the subspaces with conformal weights less than or equal to $1$ is also considered. Comment: 28 pages |
| Databáze: | OpenAIRE |
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