Finding cocycles in the bicrossed product construction for Lie groups

Abstract

We find an explicit formula for finding pairs of cocycles for the construction of examples of locally compact quantum groups by using the bicrossed product of Lie groups.

Construction of continuous cocycles for the bicrossed product of locally compact groups

“…Then f is equivalent to the normalized cocycle specified by the right-hand side of (47) independent of m 1 and n 3 , i.e., satisfying (8). This means that the right-hand side of (47) specifies an element from M Z 3 N (K) and, hence, an element from E(M, N ), which completes the proof.…”

“…Thus, we denote by M Z 3 N (K) a subgroup of 3-cocycles in Z 3 (K) satisfying condition (8) and consider the group E(M, N ) as M Z 3 N (K)/ ∼, where the equivalence relation ∼ is defined by relations (7) and (6).…”

“…Another algorithm for the determination of pairs of cocycles for Lie groups, under certain additional conditions, is proposed in [8] (see also [9]). …”