$\mathcal{L}$-- and $\mathcal{R}$--cross-sections in the Brauer semigoup

Details $\mathcal{L}$-- and $\mathcal{R}$--cross-sections in the Brauer semigoup $\mathcal{L}$-- and $\mathcal{R}$--cross-sections in the Brauer semigoup

2004-11-24

arxiv.org/abs/math/0411548v2

Semigroup Forum 72 (2006), no. 2, 223-248

Mathematics

Group Theory

21 page, 5 figures

Scientific paper

We classify all cross-sections of Green's relations $\mathcal{L}$ and $\mathcal{R}$ in the Brauer semigroup. The regular behavior of such cross-sections starts from $n=7$. We show that in the regular case there are essentially two different cross-sections and all others are $\mathcal{S}_n$-conjugated to one of these two. We also classify all cross-sections up to isomorphism.

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