Simplicial structures in higher Auslander-Reiten theory
(2019) In Advances in Mathematics 355.- Abstract
- We develop a novel combinatorial perspective on the higher Auslander algebras of type A, a family of algebras arising in the context of Iyama's higher Auslander–Reiten theory. This approach reveals interesting simplicial structures hidden within the representation theory of these algebras and establishes direct connections to Eilenberg–MacLane spaces and higher-dimensional versions of Waldhausen's S-construction in algebraic K-theory. As an application of our techniques we provide a generalisation of the higher reflection functors of Iyama and Oppermann to representations with values in stable infinity-categories. The resulting combinatorial framework of slice mutation can be regarded as a higher-dimensional variant of the abstract... (More)
- We develop a novel combinatorial perspective on the higher Auslander algebras of type A, a family of algebras arising in the context of Iyama's higher Auslander–Reiten theory. This approach reveals interesting simplicial structures hidden within the representation theory of these algebras and establishes direct connections to Eilenberg–MacLane spaces and higher-dimensional versions of Waldhausen's S-construction in algebraic K-theory. As an application of our techniques we provide a generalisation of the higher reflection functors of Iyama and Oppermann to representations with values in stable infinity-categories. The resulting combinatorial framework of slice mutation can be regarded as a higher-dimensional variant of the abstract representation theory of type quivers developed by Groth and Šťovíček. Our simplicial point of view then naturally leads to an interplay between slice mutation, horn filling conditions, and the higher Segal conditions of Dyckerhoff and Kapranov. In this context, we provide a classification of higher Segal objects with values in any abelian category or stable infinity-category. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/f264539e-870e-4cc0-b307-bddeeb9a5be5
- author
- Dyckerhoff, Tobias ; Jasso, Gustavo LU and Walde, Tashi
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Higher Auslander algebras, Higher Segal spaces, Tilting, Dold-Kan correspondence
- in
- Advances in Mathematics
- volume
- 355
- article number
- 106762
- pages
- 73 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85070678684
- ISSN
- 0001-8708
- DOI
- 10.1016/j.aim.2019.106762
- language
- English
- LU publication?
- no
- id
- f264539e-870e-4cc0-b307-bddeeb9a5be5
- date added to LUP
- 2022-03-09 15:02:57
- date last changed
- 2022-05-04 04:24:20
@article{f264539e-870e-4cc0-b307-bddeeb9a5be5,
abstract = {{We develop a novel combinatorial perspective on the higher Auslander algebras of type A, a family of algebras arising in the context of Iyama's higher Auslander–Reiten theory. This approach reveals interesting simplicial structures hidden within the representation theory of these algebras and establishes direct connections to Eilenberg–MacLane spaces and higher-dimensional versions of Waldhausen's S-construction in algebraic K-theory. As an application of our techniques we provide a generalisation of the higher reflection functors of Iyama and Oppermann to representations with values in stable infinity-categories. The resulting combinatorial framework of slice mutation can be regarded as a higher-dimensional variant of the abstract representation theory of type quivers developed by Groth and Šťovíček. Our simplicial point of view then naturally leads to an interplay between slice mutation, horn filling conditions, and the higher Segal conditions of Dyckerhoff and Kapranov. In this context, we provide a classification of higher Segal objects with values in any abelian category or stable infinity-category.}},
author = {{Dyckerhoff, Tobias and Jasso, Gustavo and Walde, Tashi}},
issn = {{0001-8708}},
keywords = {{Higher Auslander algebras; Higher Segal spaces; Tilting; Dold-Kan correspondence}},
language = {{eng}},
publisher = {{Elsevier}},
series = {{Advances in Mathematics}},
title = {{Simplicial structures in higher Auslander-Reiten theory}},
url = {{http://dx.doi.org/10.1016/j.aim.2019.106762}},
doi = {{10.1016/j.aim.2019.106762}},
volume = {{355}},
year = {{2019}},
}