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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.06209 |
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| _version_ | 1866915767666081792 |
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| author | Kang, Seok-Jin Kim, Young Rock Tong, Bolun |
| author_facet | Kang, Seok-Jin Kim, Young Rock Tong, Bolun |
| contents | We categorify a class of quantum groups associated with quivers, possibly with loops, by constructing the corresponding Khovanov-Lauda-Rouquier algebras (KLR) algebras $R$. We prove that the indecomposable projective $R$-modules realize the canonical basis of the negative part $U^-$ of the quantum group. Moreover, for $Λ\in P^+$, the cyclotomic KLR algebra $R^Λ$ provide a categorification of the irreducible highest weight $U$-module $V(Λ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06209 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum groups of Borcherds-Cartan type and Khovanov-Lauda-Rouquier algebras Kang, Seok-Jin Kim, Young Rock Tong, Bolun Quantum Algebra We categorify a class of quantum groups associated with quivers, possibly with loops, by constructing the corresponding Khovanov-Lauda-Rouquier algebras (KLR) algebras $R$. We prove that the indecomposable projective $R$-modules realize the canonical basis of the negative part $U^-$ of the quantum group. Moreover, for $Λ\in P^+$, the cyclotomic KLR algebra $R^Λ$ provide a categorification of the irreducible highest weight $U$-module $V(Λ)$. |
| title | Quantum groups of Borcherds-Cartan type and Khovanov-Lauda-Rouquier algebras |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2501.06209 |