Donovan’s conjecture, crossed products and algebraic group actions
Donovan’s conjecture, crossed products and algebraic group actions
复制标题
多诺万猜想、交叉积和代数群行动
DOI：
10.1007/bf02762084
复制
发表时间：
1995
影响因子：
1
通讯作者：
B. Külshammer
中科院分区：
文献类型：
--
作者：
B. Külshammer
Donovan猜想，关于素特征p的代数闭域上的有限群代数的块，断言对于任何有限群D，只有1000个Morita等价类的块具有亏群D。本文的主要结果是一个约化定理：它足以证明D的共轭生成群的猜想。沿着证明了其他一些有限性结果。主要的工具是一个结果的行动的代数群。
Donovan’s conjecture, on blocks of finite group algebras over an algebraically closed field of prime characteristicp, asserts that for any finitep-groupD, there are only finitely many Morita equivalence classes of blocks with defect groupD. The main result of this paper is a reduction theorem: It suffices to prove the conjecture for groups generated by conjugates ofD. A number of other finiteness results are proved along the way. The main tool is a result on actions of algebraic groups.