Details
| Original language | English |
|---|---|
| Pages (from-to) | 483-494 |
| Number of pages | 12 |
| Journal | Journal of algebra |
| Volume | 589 |
| Early online date | 21 Jul 2021 |
| Publication status | Published - 2022 |
| Externally published | Yes |
Abstract
Let G=SL(2,5) be the special linear group of 2×2-matrices with coefficients in the field with 5 elements. We show that the principal block over a splitting field K of characteristic two of the group algebra KG has a 3-cluster tilting module. This gives the first example of a representation-infinite block of a group algebra having a cluster tilting module and answers a question by Erdmann and Holm.
Keywords
- Algebras of quaternion type, Cluster tilting modules, Group algebras
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of algebra, Vol. 589, 2022, p. 483-494.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A cluster tilting module for a representation-infinite block of a group algebra
AU - Böhmler, Bernhard
AU - Marczinzik, René
N1 - Funding Information: We thank Karin Erdmann for having informed us in private communication that she has also found a 3-cluster tilting module for another algebra of quaternion type which is not a block of a group algebra, see also [5] . We thank Thorsten Holm for providing a reference to his habilitation thesis. We thank the anonymous referee for useful suggestions, in particular for the recommendation to add a theoretic argument for the existence of a 3-cluster tilting module. Bernhard Böhmler gratefully acknowledges funding by the DFG ( SFB/TRR 195 ). René Marczinzik gratefully acknowledges funding by the DFG (with project number 428999796 ). We profited from the use of the GAP-package [15] .
PY - 2022
Y1 - 2022
N2 - Let G=SL(2,5) be the special linear group of 2×2-matrices with coefficients in the field with 5 elements. We show that the principal block over a splitting field K of characteristic two of the group algebra KG has a 3-cluster tilting module. This gives the first example of a representation-infinite block of a group algebra having a cluster tilting module and answers a question by Erdmann and Holm.
AB - Let G=SL(2,5) be the special linear group of 2×2-matrices with coefficients in the field with 5 elements. We show that the principal block over a splitting field K of characteristic two of the group algebra KG has a 3-cluster tilting module. This gives the first example of a representation-infinite block of a group algebra having a cluster tilting module and answers a question by Erdmann and Holm.
KW - Algebras of quaternion type
KW - Cluster tilting modules
KW - Group algebras
UR - http://www.scopus.com/inward/record.url?scp=85111320575&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2101.10217
DO - 10.48550/arXiv.2101.10217
M3 - Article
VL - 589
SP - 483
EP - 494
JO - Journal of algebra
JF - Journal of algebra
SN - 0021-8693
ER -