A type Q Kac-Moody construction
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| _version_ | 1866918481671225344 |
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| author | Sherman, Alexander Silberberg, Lior |
| author_facet | Sherman, Alexander Silberberg, Lior |
| contents | We introduce a new, Kac--Moody-flavoured construction for Lie superalgebras, which incorporates phenomena of the type Q (queer) Lie superalgebra. This is done by replacing a maximal even torus by the most general possible Cartan subalgebra for Lie superalgebras, which is a maximal quasitoral subalgebra. The theory is remarkably rigid but nevertheless unveils a new natural class of Lie superalgebras, which we call type Q Kac--Moody (QKM) algebras. We classify finite-growth type Q Kac--Moody algebras, and obtain in a novel way the $d=2$, $\mathcal{N}=1,2,3,4$ twisted superconformal algebras, along with three other new, finite growth Lie superalgebras. Our work also gives a new perspective on the distinctiveness of the Lie superalgebra $\mathfrak{q}(n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09559 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A type Q Kac-Moody construction Sherman, Alexander Silberberg, Lior Representation Theory Mathematical Physics We introduce a new, Kac--Moody-flavoured construction for Lie superalgebras, which incorporates phenomena of the type Q (queer) Lie superalgebra. This is done by replacing a maximal even torus by the most general possible Cartan subalgebra for Lie superalgebras, which is a maximal quasitoral subalgebra. The theory is remarkably rigid but nevertheless unveils a new natural class of Lie superalgebras, which we call type Q Kac--Moody (QKM) algebras. We classify finite-growth type Q Kac--Moody algebras, and obtain in a novel way the $d=2$, $\mathcal{N}=1,2,3,4$ twisted superconformal algebras, along with three other new, finite growth Lie superalgebras. Our work also gives a new perspective on the distinctiveness of the Lie superalgebra $\mathfrak{q}(n)$. |
| title | A type Q Kac-Moody construction |
| topic | Representation Theory Mathematical Physics |
| url | https://arxiv.org/abs/2309.09559 |