Quantization of locally compact groups associated with essentially bijective \(1\)-cocycles (Q6563068)

The present paper is a continuation of the paper [the authors, J. Funct. Anal. 280, No. 4, Article ID 108844, 53 p. (2021; Zbl 1467.46068)]. Let a locally compact group \(Q\) act on an abelian locally compact group \(V\). Let \(G\) be an extension of \(V\) by \(Q\). Let also be given an essentially bijective \(1\)-cocycle \(\eta: Q\rightarrow \hat{V}\). Then the authors define a dual unitary \(2\)-cocycle on \(G\) and show that the associated deformation of \(\hat{G}\) is a cocycle bicrossed product defined by a matched pair of subgroups of the semi-direct product of \(Q\) and \(\hat{V}\). As a consequence, the authors obtain a locally compact quantum group from every involutive non-degenerate set-theoretical solution of the Yang-Baxter equation.