Regular representations of infinite dimensional group \(B_0^\mathbb Z\) and factors (Q2784965)

An analog of the regular representation for the group \(B_0^\mathbb Z\) of upper triangular matrices that are infinite in both directions with units on the principal diagonal and a finite number of non-zero elements in each row and column was introduced by \textit{A. V. Kosyak} [Sel. Math. Sov. 11, 241-291 (1992; Zbl 0798.22008)]. The representation is determined by a Gaussian measure on a wider group \(B^\mathbb Z\) (defined similarly, but without the finiteness condition). The authors find conditions on the measure under which the von Neumann algebra generated by the above representation is a factor.