Higher Nakayama algebras I : Construction
(2019) In Advances in Mathematics 351. p.1139-1200- Abstract
- We introduce higher dimensional analogues of the Nakayama algebras from the viewpoint of Iyama's higher Auslander–Reiten theory. More precisely, for each Nakayama algebra A and each positive integer d, we construct a finite dimensional algebra A(d) having a distinguished d-cluster-tilting -module whose endomorphism algebra is a higher dimensional analogue of the Auslander algebra of A. We also construct higher dimensional analogues of the mesh category of type ZA_infinity and the tubes.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/198ef02b-0db4-4398-a370-b23e6acb9b38
- author
- Jasso, Gustavo LU and Külshammer, Julian
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Auslander–Reiten theory, Auslander–Reiten quiver, Nakayama algebras, Cluster-tilting, Homological embedding
- in
- Advances in Mathematics
- volume
- 351
- pages
- 62 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85066485799
- ISSN
- 0001-8708
- DOI
- 10.1016/j.aim.2019.05.026
- language
- English
- LU publication?
- no
- additional info
- With an appendix by Julian Külshammer and Chrysostomos Psaroudakis and an appendix by Sondre Kvamme.
- id
- 198ef02b-0db4-4398-a370-b23e6acb9b38
- date added to LUP
- 2022-03-09 15:04:33
- date last changed
- 2022-04-22 00:27:23
@article{198ef02b-0db4-4398-a370-b23e6acb9b38, abstract = {{We introduce higher dimensional analogues of the Nakayama algebras from the viewpoint of Iyama's higher Auslander–Reiten theory. More precisely, for each Nakayama algebra A and each positive integer d, we construct a finite dimensional algebra A(d) having a distinguished d-cluster-tilting -module whose endomorphism algebra is a higher dimensional analogue of the Auslander algebra of A. We also construct higher dimensional analogues of the mesh category of type ZA_infinity and the tubes.}}, author = {{Jasso, Gustavo and Külshammer, Julian}}, issn = {{0001-8708}}, keywords = {{Auslander–Reiten theory; Auslander–Reiten quiver; Nakayama algebras; Cluster-tilting; Homological embedding}}, language = {{eng}}, pages = {{1139--1200}}, publisher = {{Elsevier}}, series = {{Advances in Mathematics}}, title = {{Higher Nakayama algebras I : Construction}}, url = {{http://dx.doi.org/10.1016/j.aim.2019.05.026}}, doi = {{10.1016/j.aim.2019.05.026}}, volume = {{351}}, year = {{2019}}, }