Double Yangian and reflection algebras of the Lie superalgebra $\mathfrak{gl}_{m|n}$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909422586953728 |
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| author | Bagnoli, Lucia Kožić, Slaven |
| author_facet | Bagnoli, Lucia Kožić, Slaven |
| contents | We study the double Yangian associated with the Lie superalgebra $\mathfrak{gl}_{m|n}$. Our main focus is on establishing the Poincaré-Birkhoff-Witt Theorem for the double Yangian and constructing its central elements in the form of coefficients of the quantum contraction. Next, as an application, we introduce reflection algebras, certain left coideal subalgebras of the level 0 double Yangian, and find their presentations by generators and relations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02410 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Double Yangian and reflection algebras of the Lie superalgebra $\mathfrak{gl}_{m|n}$ Bagnoli, Lucia Kožić, Slaven Quantum Algebra Mathematical Physics Representation Theory We study the double Yangian associated with the Lie superalgebra $\mathfrak{gl}_{m|n}$. Our main focus is on establishing the Poincaré-Birkhoff-Witt Theorem for the double Yangian and constructing its central elements in the form of coefficients of the quantum contraction. Next, as an application, we introduce reflection algebras, certain left coideal subalgebras of the level 0 double Yangian, and find their presentations by generators and relations. |
| title | Double Yangian and reflection algebras of the Lie superalgebra $\mathfrak{gl}_{m|n}$ |
| topic | Quantum Algebra Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2311.02410 |