自由群von Neumann代数的L^(p)分解

L^(p)-decomposition of free group von Neumann algebras

本文研究基于n阶自由群Fn的非交换L^(p)空间,对于n=2和n=∞,给出所对应非交换L^(p)空间互相同构的一个新证明,并给出该同构的具体形式.进一步讨论自由群von Neumann代数的L^(p)分解与von Neumann代数刚性问题的联系.

We study the noncommutative L^(p)-spaces associated with the von Neumann algebras of rank n free groups.The main result is a new proof of the isomorphism relation between the noncommutative L^(p)-spaces for n=2 and n=1.The advantage of this new proof is that it gives the concrete form of the isomorphism maps.We further discuss the L^(p)-decomposition of free group von Neumann algebras and its relation to the von Neumann rigidity problem of free groups.