The symplectic geometry of higher Auslander algebras: Symmetric products of disks
(2021) In Forum of Mathematics, Sigma 9.- Abstract
- We show that the perfect derived categories of Iyama’s d-dimensional Auslander algebras of type A are equivalent to the partially wrapped Fukaya categories of the d-fold symmetric product of the 2-dimensional unit disk with finitely many stops on its boundary. Furthermore, we observe that Koszul duality provides an equivalence between the partially wrapped Fukaya categories associated to the d-fold symmetric product of the disk and those of its (n−d)-fold symmetric product; this observation leads to a symplectic proof of a theorem of Beckert concerning the derived Morita equivalence between the corresponding higher Auslander algebras of type A. As a by-product of our results, we deduce that the partially wrapped Fukaya categories... (More)
- We show that the perfect derived categories of Iyama’s d-dimensional Auslander algebras of type A are equivalent to the partially wrapped Fukaya categories of the d-fold symmetric product of the 2-dimensional unit disk with finitely many stops on its boundary. Furthermore, we observe that Koszul duality provides an equivalence between the partially wrapped Fukaya categories associated to the d-fold symmetric product of the disk and those of its (n−d)-fold symmetric product; this observation leads to a symplectic proof of a theorem of Beckert concerning the derived Morita equivalence between the corresponding higher Auslander algebras of type A. As a by-product of our results, we deduce that the partially wrapped Fukaya categories associated to the d-fold symmetric product of the disk organise into a paracyclic object equivalent to the d-dimensional Waldhausen S-dot-construction, a simplicial space whose geometric realisation provides the d-fold delooping of the connective algebraic K-theory space of the ring of coefficients.
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Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/7b9a0378-9c4c-4062-b81d-1b5fd5a0820f
- author
- Dyckerhoff, Tobias ; Jasso, Gustavo LU and Lekili, Yanki
- publishing date
- 2021-02-01
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Forum of Mathematics, Sigma
- volume
- 9
- article number
- e10
- pages
- 49 pages
- publisher
- Cambridge University Press
- external identifiers
-
- scopus:85102142135
- DOI
- 10.1017/fms.2021.2
- language
- English
- LU publication?
- no
- id
- 7b9a0378-9c4c-4062-b81d-1b5fd5a0820f
- date added to LUP
- 2022-03-09 14:55:59
- date last changed
- 2022-10-04 04:12:42
@article{7b9a0378-9c4c-4062-b81d-1b5fd5a0820f,
abstract = {{We show that the perfect derived categories of Iyama’s d-dimensional Auslander algebras of type A are equivalent to the partially wrapped Fukaya categories of the d-fold symmetric product of the 2-dimensional unit disk with finitely many stops on its boundary. Furthermore, we observe that Koszul duality provides an equivalence between the partially wrapped Fukaya categories associated to the d-fold symmetric product of the disk and those of its (n−d)-fold symmetric product; this observation leads to a symplectic proof of a theorem of Beckert concerning the derived Morita equivalence between the corresponding higher Auslander algebras of type A. As a by-product of our results, we deduce that the partially wrapped Fukaya categories associated to the d-fold symmetric product of the disk organise into a paracyclic object equivalent to the d-dimensional Waldhausen S-dot-construction, a simplicial space whose geometric realisation provides the d-fold delooping of the connective algebraic K-theory space of the ring of coefficients.<br/>}},
author = {{Dyckerhoff, Tobias and Jasso, Gustavo and Lekili, Yanki}},
language = {{eng}},
month = {{02}},
publisher = {{Cambridge University Press}},
series = {{Forum of Mathematics, Sigma}},
title = {{The symplectic geometry of higher Auslander algebras: Symmetric products of disks}},
url = {{http://dx.doi.org/10.1017/fms.2021.2}},
doi = {{10.1017/fms.2021.2}},
volume = {{9}},
year = {{2021}},
}