## 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**

## Cite this

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**A cluster tilting module for a representation-infinite block of a group algebra.**/ Böhmler, Bernhard; Marczinzik, René.

In: Journal of algebra, Vol. 589, 2022, p. 483-494.

Research output: Contribution to journal › Article › Research › peer review

*Journal of algebra*, vol. 589, pp. 483-494. https://doi.org/10.48550/arXiv.2101.10217, https://doi.org/10.1016/j.jalgebra.2021.06.037

}

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 -