Splendid Derived Equivalences for Blocks of Finite p‐Solvable Groups
Splendid Derived Equivalences for Blocks of Finite p‐Solvable Groups
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DOI：
10.1112/s0024610700008966
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发表时间：
2000-08
期刊：
影响因子：
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通讯作者：
M. E. Harris;M. Linckelmann
中科院分区：
文献类型：
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作者：
M. E. Harris;M. Linckelmann
自从J. Rickard在[15，16]中发现了有限群的p-块理论中导出等价的相关性，其中p是素数，已经进行了各种尝试来理解这种现象。特别地，J. Rickard在[18]中定义了有限群的p-块的导出模范畴之间的某类导出等价，他称之为辉煌等价。（我们在本文中称之为精彩的导出等价），它考虑了局部结构，即，在适当的假设下，在所考虑的p-块的所有“局部水平”上诱导出一系列导出的等价物（更详细的动机见[18]）。一个导出的等价是极好的主要条件是它是由一个由p置换双模组成的双侧倾斜复形给出的（精确术语见下面的定义1.3和1.4）。
Since the remarkable discovery of the relevance of derived equivalences in the theory of p‐blocks of finite groups, where p is a prime, by J. Rickard in [15, 16], various attempts have been made to understand this phenomenon. In particular, J. Rickard defines in [18] a certain class of derived equivalences between the derived module categories of p‐blocks of finite groups that he calls splendid equivalences (and that we are going to call splendid derived equivalences in this paper) which take into account the local structure, that is, which under suitable hypotheses induce a family of derived equivalences at all ‘local levels’ of the considered p‐blocks (see [18] for a more detailed motivation). The main condition for a derived equivalence to be splendid is that it is given by a two‐sided tilting complex consisting of p‐permutation bimodules (see Definitions 1.3 and 1.4 below for the precise terminology).