Splendid Morita equivalences for principal 2-blocks with dihedral defect groups

被引：8

作者：

Koshitani, Shigeo ^{[1
]}

Lassueur, Caroline ^{[2
]}

机构：

[1] Chiba Univ, Ctr Frontier Sci, Inage Ku, 1-33 Yayoi Cho, Chiba 2638522, Japan

[2] TU Kaiserslautern, FB Math, Postfach 3049, Kaiserslautern 67653, Germany

来源：

MATHEMATISCHE ZEITSCHRIFT | 2020年 / 294卷 / 1-2期

关键词：

Puig's finiteness conjecture; Morita equivalence; Splendid Morita equivalence; Stable equivalence of Morita type; Scott module; Brauer indecomposability; Generalised decomposition numbers; Dihedral; 2-group; BRAUER INDECOMPOSABILITY; SCOPES REDUCTION; STABLE EQUIVALENCES; CONJECTURE HOLDS; FUSION SYSTEMS; SCOTT MODULES; BLOCKS; CHARACTERS; ALGEBRAS; COVERS;

D O I：

10.1007/s00209-019-02301-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a dihedral 2-group P of order at least 8, we classify the splendid Morita equivalence classes of principal 2-blocks with defect groups isomorphic to P. To this end we construct explicit stable equivalences of Morita type induced by specific Scott modules using Brauer indecomposability and gluing methods; we then determine when these stable equivalences are actually Morita equivalences, and hence automatically splendid Morita equivalences. Finally, we compute the generalised decomposition numbers in each case.

引用

页码：639 / 666

页数：28

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