Blocks inequivalent to their Frobenius twists
Blocks inequivalent to their Frobenius twists
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与弗罗贝尼乌斯扭曲不等价的块
DOI：
10.1016/j.jalgebra.2007.03.044
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发表时间：
2007
影响因子：
0.9
通讯作者：
R. Kessar
中科院分区：
文献类型：
--
作者：
D. Benson;R. Kessar
设k是特征为p的代数闭域，给出了有限群代数块B不与Frobenius扭曲B(P)的k-代数Morita等价的例子的一般产生方法。我们的方法产生具有一个单模和基本阿贝尔亏群的非幂零块。它们还提供了第一个已知的块的例子，其中在普通字符级别上存在完美的同型，所有符号都是正的，但块之间没有派生的等价性。我们不知道有任何块B的例子不是森田等价于第二弗罗贝尼乌斯扭转[公式：见正文]。
Let k be an algebraically closed field of characteristic p. We give a general method for producing examples of blocks B of finite group algebras that are not Morita equivalent as k-algebras to the Frobenius twist B(p). Our method produces non-nilpotent blocks having one simple module and elementary abelian defect group. These also provide the first known examples of blocks where there is a perfect isotypy at the level of ordinary characters with all the signs positive, but no derived equivalence between the blocks. We do not know of any examples of blocks B that are not Morita equivalent to the second Frobenius twist [Formula: see text] .