Strong Morita Equivalence of Inverse Semigroups
Strong Morita Equivalence of Inverse Semigroups
复制标题
逆半群的强森田等价
DOI：
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发表时间：
2009
期刊：
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通讯作者：
B. Steinberg
中科院分区：
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作者：
B. Steinberg
引入了逆半群的强Morita等价。这个概念包含了马克·劳森的扩张概念。强Morita等价逆半群具有Paterson意义下的Morita等价泛广群胚，因此是强Morita等价泛约化$C^*$-代数。作为结果，我们得到了Khoshkam和Skandalis关于$F$-逆半群的$C^*$-代数是交换$C^*$-代数与群的叉积的强Morita等价的结果的一个新证明.
We introduce strong Morita equivalence for inverse semigroups. This notion encompasses Mark Lawson's concept of enlargement. Strongly Morita equivalent inverse semigroups have Morita equivalent universal groupoids in the sense of Paterson and hence strongly Morita equivalent universal and reduced $C^*$-algebras. As a consequence we obtain a new proof of a result of Khoshkam and Skandalis showing that the $C^*$-algebra of an $F$-inverse semigroup is strongly Morita equivalent to a cross product of a commutative $C^*$-algebra by a group.