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▫$\cal L$▫- and ▫$\cal R$▫-cross-sections in the Brauer semigroup
Kudryavtseva, Ganna ; Maltcev, Victor ; Mazorchuk, Volodymyr
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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