Drinfeld super Yangian of the exceptional Lie superalgebra $D(2,1;λ)$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918005180465152 |
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| author | Lin, Hongda Zhang, Honglian |
| author_facet | Lin, Hongda Zhang, Honglian |
| contents | In this paper, we establish the first rigorous framework for the Drinfeld super Yangian associated with an exceptional Lie superalgebra, which lacks a classical Lie algebraic counterpart. Specifically, we systematically investigate the Drinfeld presentation and structural properties of the super Yangian associated with the exceptional Lie superalgebra $D(2,1;λ)$. First, we introduce a Drinfeld presentation for the super Yangian associated with the exceptional Lie superalgebra $D(2,1;λ)$, explicitly constructing its current generators and defining relations. A key innovation is the construction of a Poincaré-Birkhoff-Witt (PBW) basis using degeneration techniques from the corresponding quantum loop superalgebra. Furthermore, we demonstrate that the super Yangian possesses a Hopf superalgebra structure, explicitly providing the coproduct, counit, and antipode. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21255 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Drinfeld super Yangian of the exceptional Lie superalgebra $D(2,1;λ)$ Lin, Hongda Zhang, Honglian Quantum Algebra Mathematical Physics Rings and Algebras In this paper, we establish the first rigorous framework for the Drinfeld super Yangian associated with an exceptional Lie superalgebra, which lacks a classical Lie algebraic counterpart. Specifically, we systematically investigate the Drinfeld presentation and structural properties of the super Yangian associated with the exceptional Lie superalgebra $D(2,1;λ)$. First, we introduce a Drinfeld presentation for the super Yangian associated with the exceptional Lie superalgebra $D(2,1;λ)$, explicitly constructing its current generators and defining relations. A key innovation is the construction of a Poincaré-Birkhoff-Witt (PBW) basis using degeneration techniques from the corresponding quantum loop superalgebra. Furthermore, we demonstrate that the super Yangian possesses a Hopf superalgebra structure, explicitly providing the coproduct, counit, and antipode. |
| title | Drinfeld super Yangian of the exceptional Lie superalgebra $D(2,1;λ)$ |
| topic | Quantum Algebra Mathematical Physics Rings and Algebras |
| url | https://arxiv.org/abs/2504.21255 |