Invariant Hermitian forms on vertex algebras
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2020
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916343082647552 |
|---|---|
| author | Kac, Victor G. Frajria, Pierluigi Möseneder Papi, Paolo |
| author_facet | Kac, Victor G. Frajria, Pierluigi Möseneder Papi, Paolo |
| contents | We study invariant Hermitian forms on a conformal vertex algebra and on their (twisted) modules. We establish existence of a non-zero invariant Hermitian form on an arbitrary $W$-algebra. We show that for a minimal simple $W$-algebra $W_k(\mathfrak g,θ/2)$ this form can be unitary only when its $\tfrac{1}{2}\mathbb Z$-grading is compatible with parity, unless $W_k(\mathfrak g,θ/2)$ "collapses" to its affine subalgebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_13178 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Invariant Hermitian forms on vertex algebras Kac, Victor G. Frajria, Pierluigi Möseneder Papi, Paolo Representation Theory We study invariant Hermitian forms on a conformal vertex algebra and on their (twisted) modules. We establish existence of a non-zero invariant Hermitian form on an arbitrary $W$-algebra. We show that for a minimal simple $W$-algebra $W_k(\mathfrak g,θ/2)$ this form can be unitary only when its $\tfrac{1}{2}\mathbb Z$-grading is compatible with parity, unless $W_k(\mathfrak g,θ/2)$ "collapses" to its affine subalgebra. |
| title | Invariant Hermitian forms on vertex algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2008.13178 |