$\imath$Hall algebras of weighted projective lines and quantum symmetric pairs II: injectivity
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911771251441664 |
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| author | Lu, Ming Ruan, Shiquan |
| author_facet | Lu, Ming Ruan, Shiquan |
| contents | We show that the morphism $Ω$ from the $\imath$quantum loop algebra $^{\texttt{Dr}}\widetilde{\mathbf{U}}(L\mathfrak{g})$ of split type to the $\imath$Hall algebra of the weighted projective line is injective if $\mathfrak{g}$ is of finite or affine type. As a byproduct, we use the whole $\imath$Hall algebra of the cyclic quiver $C_n$ to realise the $\imath$quantum loop algebra of affine $\mathfrak{gl}_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03322 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\imath$Hall algebras of weighted projective lines and quantum symmetric pairs II: injectivity Lu, Ming Ruan, Shiquan Representation Theory Quantum Algebra We show that the morphism $Ω$ from the $\imath$quantum loop algebra $^{\texttt{Dr}}\widetilde{\mathbf{U}}(L\mathfrak{g})$ of split type to the $\imath$Hall algebra of the weighted projective line is injective if $\mathfrak{g}$ is of finite or affine type. As a byproduct, we use the whole $\imath$Hall algebra of the cyclic quiver $C_n$ to realise the $\imath$quantum loop algebra of affine $\mathfrak{gl}_n$. |
| title | $\imath$Hall algebras of weighted projective lines and quantum symmetric pairs II: injectivity |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2402.03322 |