## Abdulla Aljouiee

## On the Brauer Monoid of S_{3}

## (Lobachevskii Journal of Mathematics, Vol.14, pp.3-16)

Recently the authors showed that the Brauer monoid of a finite Galois group
can be written as a disjoint union of smaller pieces (groups). Each group can
be computed following Stimets by defining a chain complex and checking its
exactness. However, this method is not so encouraging because of the
difficulty of dealing with such computations even with small groups.
Unfortunately, this is the only known method so far. This paper is to apply
Stimets' method to some idempotent weak 2-cocycles defined on $S_3$. In
particular, the idempotent 2-cocycles whose associated graphs have two
generators. Some nice results appear in the theory of noncommutative
polynomials.

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