We study the von Neumann algebra, generated by the unitary representations of infinite-dimensional groups nilpotent group
. The conditions of the irreducibility of the regular and quasiregular representations of infinite-dimensional groups (associated with some quasi-invariant measures) are given by the so-called Ismagilov conjecture (see [1,2,9-11]). In this case the
... [Show full abstract] corresponding von Neumann algebra is type factor. When the regular representation is reducible we find the sufficient conditions on the measure for the von Neumann algebra to be factor (see [13,14]). In the present article we determine the type of corresponding factors. Namely we prove that the von Neumann algebra generated by the regular representations of infinite-dimensional nilpotent group is type hyperfinite factor. The case of the nilpotent group of infinite in both directions matrices will be studied in [6].