no. 1
A finite dimensional algebra with infinite delooping level
Kershaw, Luke1; Rickard, Jeremy1  
1 School of Mathematics, University of Bristol Fry Building, Woodland Road Bristol BS8 1UG United Kingdom
Annals of Representation Theory, Volume 1 (2024) no. 1, pp. 61-65.

We give an example of a finite dimensional algebra with infinite delooping level, based on an example of a semi-Gorenstein-projective module due to Ringel and Zhang.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/art.3
Classification: 16E10, 16G10
Keywords: delooping level, semi-Gorenstein-projective modules, finitistic dimension conjecture
Kershaw, Luke 1; Rickard, Jeremy 1

1 School of Mathematics, University of Bristol Fry Building, Woodland Road Bristol BS8 1UG United Kingdom
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
@article{ART_2024__1_1_61_0,
     author = {Kershaw, Luke and Rickard, Jeremy},
     title = {A finite dimensional algebra with infinite delooping level},
     journal = {Annals of Representation Theory},
     pages = {61--65},
     publisher = {The Publishers of ART},
     volume = {1},
     number = {1},
     year = {2024},
     doi = {10.5802/art.3},
     language = {en},
     url = {https://art.centre-mersenne.org/articles/10.5802/art.3/}
}
TY  - JOUR
AU  - Kershaw, Luke
AU  - Rickard, Jeremy
TI  - A finite dimensional algebra with infinite delooping level
JO  - Annals of Representation Theory
PY  - 2024
SP  - 61
EP  - 65
VL  - 1
IS  - 1
PB  - The Publishers of ART
UR  - https://art.centre-mersenne.org/articles/10.5802/art.3/
DO  - 10.5802/art.3
LA  - en
ID  - ART_2024__1_1_61_0
ER  - 
%0 Journal Article
%A Kershaw, Luke
%A Rickard, Jeremy
%T A finite dimensional algebra with infinite delooping level
%J Annals of Representation Theory
%D 2024
%P 61-65
%V 1
%N 1
%I The Publishers of ART
%U https://art.centre-mersenne.org/articles/10.5802/art.3/
%R 10.5802/art.3
%G en
%F ART_2024__1_1_61_0
Kershaw, Luke; Rickard, Jeremy. A finite dimensional algebra with infinite delooping level. Annals of Representation Theory, Volume 1 (2024) no. 1, pp. 61-65. doi : 10.5802/art.3. https://art.centre-mersenne.org/articles/10.5802/art.3/

[1] Auslander, Maurice; Reiten, Idun; Smalø, Sverre O. Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics, 36, Cambridge University Press, 1995 | DOI | Zbl

[2] Bass, Hyman Finitistic dimension and a homological generalization of semi-primary rings, Trans. Am. Math. Soc., Volume 95 (1960), pp. 466-488 | DOI | MR | Zbl

[3] Cummings, Charley Ring constructions and generation of the unbounded derived module category, Algebr. Represent. Theory, Volume 26 (2023) no. 1, pp. 281-315 | DOI | MR | Zbl

[4] Fossum, Robert M.; Griffith, Phillip A.; Reiten, Idun Trivial extensions of abelian categories. Homological algebra of trivial extensions of abelian categories with applications to ring theory, Lecture Notes in Mathematics, 456, Springer, 1975 | Zbl

[5] Gélinas, Vincent The depth, the delooping level and the finitistic dimension, Adv. Math., Volume 394 (2022), Paper no. 108052 | MR | Zbl

[6] Jorgensen, Liana M. David A. andŞega Independence of the total reflexivity conditions for modules, Algebr. Represent. Theory, Volume 9 (2006) no. 2, pp. 217-226 | DOI | MR | Zbl

[7] Marczinzik, René Gendo-symmetric algebras, dominant dimensions and Gorenstein homological algebra (2021) | arXiv

[8] Rickard, Jeremy Unbounded derived categories and the finitistic dimension conjecture, Adv. Math., Volume 354 (2019), Paper no. 106735, 21 pages | MR | Zbl

[9] Ringel, Claus Michael; Zhang, Pu Gorenstein-projective and semi-Gorenstein-projective modules, Algebra Number Theory, Volume 14 (2020) no. 1, pp. 1-36 | DOI | MR | Zbl

Cited by Sources: