论文标题
长度函数在复杂谎言组的亚组上成倍扭曲
Length functions exponentially distorted on subgroups of complex Lie groups
论文作者
论文摘要
我们引入了一个长度函数的概念，该函数在局部紧凑的组的（紧凑生成）亚组上呈指数扭曲。我们证明，对于连接的线性复杂谎言组，在指数和nilpotent自由基之间的正常积分子组上有一个最大长度函数的最大等效类别。此外，该类别的功能接受了与作者先前有关单词长度函数的渐近分解，即在指数自由基的情况下[J.谎言理论29：4，1045--1070，2019]。在一般情况下，我们使用通过塑形同构构建的辅助长度函数来banach pi-algebras。
We introduce a notion of a length function exponentially distorted on a (compactly generated) subgroup of a locally compact group. We prove that for a connected linear complex Lie group there is a maximum equivalence class of length functions exponentially distorted on a normal integral subgroup lying between the exponential and nilpotent radicals. Moreover, a function in this class admits an asymptotic decomposition similar to that previously found by the author for word length functions, i.e., in the case of exponential radical [J. Lie Theory 29:4, 1045--1070, 2019]. In the general case we use auxiliary length functions constructed via holomorphic homomorphisms to Banach PI-algebras.
