瑜伽运动员
The yoga of commutators
摘要：
在本论文中，我们讨论了一些最近版本的本地化方法计算的点群的代数和古典类群体。也就是说，我们描述相对本地化，普遍的本地化，和本地化完成的增强版本。除了这些方法的一般策略描述外，我们还陈述了共轭演算和换位子演算的一些典型技术结果。此外，我们还叙述了由此得到的几个最新结果，如相对标准的交换子公式，交换子关于初等生成元的有界宽度，以及同余子群的幂零滤子.总的来说，这表明本地化方法可以比预期的更有效。
英文摘要：
In the present paper we discuss some recent versions of localisation methods for calculations in the groups of points of algebraic-like and classical-like groups. Namely, we describe relative localisation, universal localisation, and enhanced versions of localisation-completion. Apart from the general strategic description of these methods, we state some typical technical results of the conjugation calculus and the commutator calculus. Also, we state several recent results obtained therewith, such as relative standard commutator formulae, bounded width of commutators, with respect to the elementary generators, and nilpotent filtrations of congruence subgroups. Overall, this shows that localisation methods can be much more efficient, than expected.
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