Toral subgroups lying in the centralizer of the group of units

Hunter, R. P.

doi:10.1090/S0002-9939-1980-0560596-3

Toral subgroups lying in the centralizer of the group of units
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Proc. Amer. Math. Soc. 79 (1980), 113-121 Request permission

Abstract:

Let S be a compact connected finite dimensional monoid whose group of units G is a compact connected Lie group. Then there is an open set W about the unit element such that any compact subgroup within W has dimension at most $\dim S - \dim G - 1$ and if any toral subgroup achieves this dimension then that toral subgroup lies in the centralizer of G. Two applications are given, one to embeddings of irreducible monoids into S.

References

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On the structure of homogroups and their applications to compact connected semigroups

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