部分作用、包络作用和部分表示的交叉积的结合性
Associativity of crossed products by partial actions, enveloping actions and partial representations
摘要：
给定群G在结合代数A上的部分作用α，我们考虑交叉积Ax_αG.利用A的理想的乘子代数，证明了若A的所有理想都是幂等的，则Ax_αG是结合的.这推广了以前关于C*-代数中Ax_αG结合性的一个结果.给出了代数上部分作用的整体扩张存在的一个判据，并利用交叉积研究了代数上群的部分作用与部分表示之间的关系.作为应用，我们赋予部分群代数交叉积结构。
英文摘要：
Given a partial action αof a group G on an associative algebra A we consider the crossed product A x_αG. Using the algebras of multipliers of ideals of A we prove that A x_αG is associative, provided that all ideals of A are idempotent. This generalizes a previous result on the associativity of A x_αG in the context of C*-algebras. We also give a criteria for the existence of a global extension of a given partial action on an algebra and use crossed products to study relations between partial actions of groups on algebras and partial representations. As an application we endow partial group algebras with crossed product structure.
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