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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.07938 |
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| _version_ | 1866918515013844992 |
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| author | Aizawa, N. Segar, J. |
| author_facet | Aizawa, N. Segar, J. |
| contents | It is known that there are two inequivalent $\mathbb{Z}_2^2$-graded $osp(1|2)$ Lie superalgebras. Their affine extensions are investigated and it is shown that one of them admits two central elements, one is non-graded and the other is $(1,1)$-graded. The affine $\mathbb{Z}_2^2$-$osp(1|2)$ algebras are used by the Sugawara construction to study possible $\mathbb{Z}_2^2$-graded extensions of the Virasoro algebra. We obtain a $\mathbb{Z}_2^2$-graded Virasoro algebra with a non-trivially graded central element. Throughout the investigation, invariant bilinear forms on $\mathbb{Z}_2^2$-graded superalgebras play a crucial role, so a theory of invariant bilinear forms is also developed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07938 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Affine extensions of $\mathbb{Z}_2^2$-graded $osp(1|2)$ and Virasoro algebra Aizawa, N. Segar, J. Mathematical Physics It is known that there are two inequivalent $\mathbb{Z}_2^2$-graded $osp(1|2)$ Lie superalgebras. Their affine extensions are investigated and it is shown that one of them admits two central elements, one is non-graded and the other is $(1,1)$-graded. The affine $\mathbb{Z}_2^2$-$osp(1|2)$ algebras are used by the Sugawara construction to study possible $\mathbb{Z}_2^2$-graded extensions of the Virasoro algebra. We obtain a $\mathbb{Z}_2^2$-graded Virasoro algebra with a non-trivially graded central element. Throughout the investigation, invariant bilinear forms on $\mathbb{Z}_2^2$-graded superalgebras play a crucial role, so a theory of invariant bilinear forms is also developed. |
| title | Affine extensions of $\mathbb{Z}_2^2$-graded $osp(1|2)$ and Virasoro algebra |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2409.07938 |