Cellularity and subdivision of KLR and weighted KLRW algebras
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866915666793070592 |
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| author | Mathas, Andrew Tubbenhauer, Daniel |
| author_facet | Mathas, Andrew Tubbenhauer, Daniel |
| contents | Weighted KLRW algebras are diagram algebras generalizing KLR algebras. This paper undertakes a systematic study of these algebras culminating in the construction of homogeneous affine cellular bases in affine types A and C, which immediately gives cellular bases for the cyclotomic quotients of these algebras. In addition, we construct subdivision homomorphisms that relate weighted KLRW algebras for different quivers. As an application we obtain new results about the (cyclotomic) KLR algebras of affine type, including (re)proving that the cyclotomic KLR algebras of type A^{(1)}_{e} and C^{(1)}_{e} are graded cellular algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_12949 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Cellularity and subdivision of KLR and weighted KLRW algebras Mathas, Andrew Tubbenhauer, Daniel Representation Theory Quantum Algebra Rings and Algebras Primary: 20C08, 20G43, Secondary: 18M30, 18N25 Weighted KLRW algebras are diagram algebras generalizing KLR algebras. This paper undertakes a systematic study of these algebras culminating in the construction of homogeneous affine cellular bases in affine types A and C, which immediately gives cellular bases for the cyclotomic quotients of these algebras. In addition, we construct subdivision homomorphisms that relate weighted KLRW algebras for different quivers. As an application we obtain new results about the (cyclotomic) KLR algebras of affine type, including (re)proving that the cyclotomic KLR algebras of type A^{(1)}_{e} and C^{(1)}_{e} are graded cellular algebras. |
| title | Cellularity and subdivision of KLR and weighted KLRW algebras |
| topic | Representation Theory Quantum Algebra Rings and Algebras Primary: 20C08, 20G43, Secondary: 18M30, 18N25 |
| url | https://arxiv.org/abs/2111.12949 |