逆半群作用的协变表示：约化与本质交叉积C*-代数的新方法
Covariant representations of actions of inverse semigroups: a new approach to the reduced and essential crossed-product C*-algebras
- Victoria University of Wellington（惠灵顿维多利亚大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过逆半群作用构造胚芽群胚及具体协变表示族，提出约化与本质交叉积C*-代数的新定义，避免双重换位子与局部乘子代数，并证明与已有定义同构。
AI中文摘要：
我们考虑一个逆半群在C*-代数$A$上的作用，并利用该作用构造一个胚芽群胚，其单位空间为$A$的谱。受群胚C*-代数表示论的启发，我们为该作用构造了一个具体的协变表示族。利用这一族表示，我们给出了约化与本质交叉积C*-代数的新定义，分别避免了取$A$的双重换位子和局部乘子代数。我们的约化交叉积与Exel、Buss和Meyer所定义的同构，且当逆半群为拟可数时，我们的本质交叉积与Kwaśniewski和Meyer所定义的同构。
英文摘要：
We consider an action of an inverse semigroup on a C*-algebra $A$ and use it to construct a groupoid of germs with unit space the spectrum of $A$. Motivated by the representation theory of C*-algebras of groupoids, we construct a concrete family of covariant representations for the action. We use this family to give new definitions of the reduced and essential crossed product C*-algebras that avoid, respectively, passing to the double commutant and local multiplier algebra of $A$. Our reduced crossed product is isomorphic to the one defined by Exel, Buss and Meyer, and when the inverse semigroup is quasi-countable our essential crossed product is isomorphic to the one defined by Kwaśniewski and Meyer.
