Hopf algebroids and Grothendieck-Verdier duality
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910323976437760 |
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| author | Allen, Robert |
| author_facet | Allen, Robert |
| contents | Grothendieck-Verdier duality is a powerful and ubiquitous structure on monoidal categories, which generalises the notion of rigidity. Hopf algebroids are a generalisation of Hopf algebras, to a non-commutative base ring. Just as the category of finite-dimensional modules over a Hopf algebra inherits rigidity from the category of vector spaces, we show that the category of finite-dimensional modules over a Hopf algebroid with bijective antipode inherits a Grothendieck-Verdier structure from the category of bimodules over its base algebra. We investigate the algebraic and categorical structure of this duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_01029 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hopf algebroids and Grothendieck-Verdier duality Allen, Robert Quantum Algebra Category Theory Representation Theory 16T05, 16B50, 18M10, 55U30 Grothendieck-Verdier duality is a powerful and ubiquitous structure on monoidal categories, which generalises the notion of rigidity. Hopf algebroids are a generalisation of Hopf algebras, to a non-commutative base ring. Just as the category of finite-dimensional modules over a Hopf algebra inherits rigidity from the category of vector spaces, we show that the category of finite-dimensional modules over a Hopf algebroid with bijective antipode inherits a Grothendieck-Verdier structure from the category of bimodules over its base algebra. We investigate the algebraic and categorical structure of this duality. |
| title | Hopf algebroids and Grothendieck-Verdier duality |
| topic | Quantum Algebra Category Theory Representation Theory 16T05, 16B50, 18M10, 55U30 |
| url | https://arxiv.org/abs/2308.01029 |