On the Brauer monoid of \(S_3\) (Q1422284)

In the paper [\textit{D. Haile, R. Larson, M. Sweedler}, Am. J. Math. 105, 689--814 (1983; Zbl 0523.13005)], it was shown that the Brauer monoid of a finite Galois group can be decomposed into a disjoint union of smaller groups. Each of these groups can be computed using Stimets' methods (see [\textit{R. Stimets}, Commun. Algebra 28, 1285--1308 (2000; Zbl 0969.12002) and ``Relative weak cohomology extensions'', J. Algebra (to appear)] for details). However, this method involves difficult computations even for small order Galois groups. In the paper under review, the author applies Stimets' method to certain idempotent weak 2-cocycles on \(S_3\).