Tight representations of semilattices and inverse semigroups
Tight representations of semilattices and inverse semigroups
复制标题
半格和逆半群的紧表示
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
R. Exel
中科院分区：
文献类型：
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作者：
R. Exel
摘要布尔逆半群是指其幂等元半格是布尔代数的逆半群。我们研究了给定逆半群的表示
AbstractBy a Boolean inverse semigroup we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse semigroup
$mathcal{S}$
in a Boolean inverse semigroup which are tight in a certain well defined technical sense. These representations are supposed to preserve as much as possible any trace of Booleanness present in the semilattice of idempotents of
$mathcal{S}$
. After observing that the Vagner–Preston representation is not tight, we exhibit a canonical tight representation for any inverse semigroup with zero, called the regular tight representation. We then tackle the question as to whether this representation is faithful, but it turns out that the answer is often negative. The lack of faithfulness is however completely understood as long as we restrict to continuous inverse semigroups, a class generalizing the E*-unitaries.