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arXiv · 2410.04502

On the structure of quantum affine superalgebra $U_{v}(A(0,2)^{(4)})$

Fengchang Li
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Abstract

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 $U_{v}(A(0,2)^{(4)})^{+}$.

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Fengchang Li. 2024-10-06. On the structure of quantum affine superalgebra $U_{v}(A(0,2)^{(4)})$. https://arxiv.org/abs/2410.04502

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