Multiplicative measures on free groups

Stability properties of multiplicative representations of free groups

We extend the construction of multiplicative representations for a free group G introduced by Kuhn and Steger (Isr. J., (144) 2004) in such a way that the new class Mult(G) so defined is stable under taking the finite direct sum, under changes of generators (and hence is Aut(G)-invariant), under restriction to and induction from a subgroup of finite index. The main tool is the detailed study of the properties of the action of a free group on its Cayley graph with respect to a change of generators, as well as the relative properties of the action of a subgroup of finite index after the choice o…

有限生成准自由群 $P$ 的自由乘法李代数 $L(P)$

The free multiplicative Lie algebra $L(P)$ for a finitely generated parafree group $P$

本文证明有限生成准自由群在特定同调条件下，其自由乘法李代数的换位子子群与下中心列同构，从而验证了 Ellis 猜想。

交换子恒等式、李乘积恒等式与乘法李代数

Commutator identities, Lie product identities, and Multiplicative Lie algebras

本文为泛交换子恒等式赋予正式含义，引入高阶Schur乘子，研究Steinberg与Chevalley乘法李代数及其自由结构，探讨其在描述泛交换子恒等式中的作用。