Journal article
Symmetric self-adjoint Hopf categories and a categorical Heisenberg double
- Abstract:
- Motivated by the work of of A. Zelevinsky on positive self-adjoint Hopf algebras, we define what we call a symmetric self-adjoint Hopf structure for a certain kind of semisimple abelian categories. It is known that every positive self-adjoint Hopf algebra admits a natural action of the associated Heisenberg double. We construct canonical morphisms lifting the relations that define this action on the algebra level and define an object that we call a categorical Heisenberg double that is a natural setting for considering these morphisms. As examples, we exhibit the symmetric self-adjoint Hopf structure on the categories of polynomial functors and equivariant polynomial functors. In the case of the category of polynomial functors we obtain categorification of the Fock space representation of the infinite-dimensional Heisenberg algebra.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 997.2KB, Terms of use)
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- Publisher copy:
- 10.1093/qmath/haw050
Authors
- Publisher:
- Oxford University Press
- Journal:
- Quarterly Journal Of Mathematics More from this journal
- Volume:
- 68
- Issue:
- 2
- Pages:
- 503-550
- Publication date:
- 2017-01-06
- DOI:
- EISSN:
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1464-3847
- ISSN:
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0033-5606
- Pubs id:
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pubs:666690
- UUID:
-
uuid:2a22de84-d880-44ff-b70c-19bb5290a98e
- Local pid:
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pubs:666690
- Source identifiers:
-
666690
- Deposit date:
-
2017-01-06
Terms of use
- Copyright holder:
- Gal and Gal
- Copyright date:
- 2017
- Notes:
- Copyright © 2017. Published by Oxford University Press. This is the accepted manuscript version of the article. The final version is available online from Oxford University Press at: https://doi.org/10.1093/qmath/haw050
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