Blocks with a generalized quaternion defect group and three simple modules over a 2-adic ring

Eisele Florian

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Blocks with a generalized quaternion defect group and three simple modules over a 2-adic ring

机译：具有广义四元数缺陷组和2 adic环上的三个简单模块的块

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摘要

We show that two blocks of generalized quaternion defect with three simple modules over a sufficiently large 2-adic ring O are Morita-equivalent if and only if the corresponding blocks over the residue field of O are Morita-equivalent. As a corollary we show that any two blocks defined over O with three simple modules and the same generalized quaternion defect group are derived equivalent. (C) 2016 Elsevier Inc. All rights reserved.

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《Journal of Algebra》 |2016年第null期|共29页
作者
Eisele Florian;
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正文语种 eng
中图分类代数、数论、组合理论;
关键词
Modular representation theory; Orders; Integral representations; Tame blocks;

机译：模块化表示理论;顺序;整体表示;Tame块;

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专利

1. Blocks with a generalized quaternion defect group and three simple modules over a 2-adic ring [J] . Eisele Florian Journal of Algebra . 2016,第Null期

机译：具有广义四元数缺陷组和2 adic环上的三个简单模块的块
2. Universal deformation rings, endo-trivial modules, and semidihedral and generalized quaternion 2-groups [J] . Bleher Frauke M., Chinburg Ted, Soto Roberto C. Journal of pure and applied algebra . 2019,第5期

机译：通用变形环，内透视模块和半发状和广义四元数2组
3. Hochschild cohomology ring of an order of a simple component of the rational group ring of the generalized quaternion group [J] . Hayami T Communications in algebra . 2008,第7期

机译：广义四元数群有理群环的简单分量的阶的Hochschild同调环
4. On Generalized (a, /3)-derivations in Rings and Modules [C] . Mohammad Ashraf, Shakir Ali, Nadeem-ur-Rehman Korea-China-Japan International Symposium on Ring Theory . 2009

机译：关于圆环和模块中的广义（A，/ 3）
5. Classification of Line Modules and Finite Dimensional Simple Modules over a Deformation of the Polynomial Ring in Three Variables [D] . Wu, Min. 2018

机译：三个变量中多项式环变形的线模块和有限维简单模块的分类
6. Structural hierarchies define toughness and defect-tolerance despite simple and mechanically inferior brittle building blocks [O] . Dipanjan Sen, Markus J. Buehler -1

机译：尽管简单且机械上较差的脆性构造块但结构层次结构仍定义了韧性和缺陷容忍度
7. Blocks with a generalized quaternion defect group and three simple modules over a 2-adic ring [O] . Eisele, Florian 2015

机译：具有广义四元数缺陷组和三个简单的块 2-adic环上的模块

Blocks with a generalized quaternion defect group and three simple modules over a 2-adic ring

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