On the structure of quantum affine superalgebra $U_{v}(A(0,2)^{(4)})$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929529512001536 |
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| author | Li, Fengchang |
| author_facet | Li, Fengchang |
| contents | We research $U_{v}(A(0,2)^{(4)})^{+}$ defined by quantum Serre relations, when $v$ is not a root of unity. We prove that $U_{v}(A(0,2)^{(4)})^{+}$ is isomorphic to a Nichols algebra. In other words, it is equivalent to define $U_{v}(A(0,2)^{(4)})^{+}$ by quantum Serre relations and by the radical of the bilinear form. We determine all the root multiplicities and give a PBW basis of $U_{v}(A(0,2)^{(4)})^{+}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_04502 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the structure of quantum affine superalgebra $U_{v}(A(0,2)^{(4)})$ Li, Fengchang Quantum Algebra 16T05, 17B37, 17B67 We research $U_{v}(A(0,2)^{(4)})^{+}$ defined by quantum Serre relations, when $v$ is not a root of unity. We prove that $U_{v}(A(0,2)^{(4)})^{+}$ is isomorphic to a Nichols algebra. In other words, it is equivalent to define $U_{v}(A(0,2)^{(4)})^{+}$ by quantum Serre relations and by the radical of the bilinear form. We determine all the root multiplicities and give a PBW basis of $U_{v}(A(0,2)^{(4)})^{+}$. |
| title | On the structure of quantum affine superalgebra $U_{v}(A(0,2)^{(4)})$ |
| topic | Quantum Algebra 16T05, 17B37, 17B67 |
| url | https://arxiv.org/abs/2410.04502 |