On the structure of modules of type $FP_\infty$

Peter H. Kropholler

Abstract:
Let $G$ be a group in the class \lhf\ of locally hierarchically 
decomposable groups and let $R$ be a strongly $G$-graded algebra.
We provide a characterization of the modules of type $FP_\infty$
under the assumptions that $R_1$ is coherent and of finite global
dimension.