Splendid Morita equivalences for principal blocks with semidihedral defect groups

Koshitani, Shigeo; Lassueur, Caroline; Sambale, Benjamin

doi:10.1090/proc/15631

Cited by 4 publications

(3 citation statements)

References 22 publications

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“…We emphasize that in the case of principal blocks of tame representation type, treated in [KL20a,KL20b,KLS22], a classification of these blocks up to Morita equivalence was known by Erdmann's work on tame algebras [Erd90]. A major difference in the case of wreathed Sylow 2-subgroups lies in the fact that a classification of these blocks up to Morita equivalence was, to our knowledge, not known.…”

Section: Introductionmentioning

confidence: 92%

“…The next theorem is a standard method, called "gluing method", which was already applied in [KL20a,KLS22]. It relies on gluing results, allowing us to construct stable equivalences of Morita type, which is a slight variation of different results of the same type due to Broué, Rouquier, Linckelmann and Rickard.…”

Section: Preliminariesmentioning

confidence: 99%

“…In a series of previous articles [KL20a,KL20b,KLS22] the authors classified principal block algebras of tame representation type up to splendid Morita equivalence, that is, in the case in which p = 2 and the Sylow 2-subgroups of the groups considered are either dihedral, semi-dihedral, or generalised quaternion 2-groups. As a corollary, the validity of Puig's conjecture is verified for this class of 2-blocks.…”

Section: Introductionmentioning

confidence: 99%

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Splendid Morita equivalences for principal blocks with generalised quaternion defect groups

Koshitani

Lassueur

2020

Journal of Algebra

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Section: Introductionmentioning

confidence: 92%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Splendid Morita equivalences for principal blocks with generalised quaternion defect groups

Koshitani

Lassueur

2020

Journal of Algebra

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Recognition of Brauer indecomposability for a Scott module

Koshitani¹,

Tuvay²

2023

J. Algebra Appl.

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We give a handy way to have a situation that the [Formula: see text]-Scott module with vertex [Formula: see text] remains indecomposable under taking the Brauer construction for any subgroup [Formula: see text] of [Formula: see text] as [Formula: see text]-module, where [Formula: see text] is a field of characteristic [Formula: see text]. The motivation is that the Brauer indecomposability of a [Formula: see text]-permutation bimodule is one of the key steps in order to obtain a splendid stable equivalence of Morita type by making use of the gluing method, that then can possibly lift to a splendid derived equivalence. Further our result explains a hidden reason why the Brauer indecomposability of the Scott module fails in Ishioka’s recent examples.

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Splendid Morita equivalences for the principal 2-blocks of 2-dimensional general linear groups in non-defining characteristic

Kunugi,

Suzuki

2023

SUT J. Math.

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Splendid Morita equivalences for principal blocks with semidihedral defect groups

Cited by 4 publications

References 22 publications

Splendid Morita equivalences for principal blocks with generalised quaternion defect groups

Splendid Morita equivalences for principal blocks with generalised quaternion defect groups

Recognition of Brauer indecomposability for a Scott module

Splendid Morita equivalences for the principal 2-blocks of 2-dimensional general linear groups in non-defining characteristic

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