标题： 相对广义布尔动力系统代数 显示英文标题

标题： Relative Generalized Boolean Dynamical System Algebras

摘要： 我们研究与广义布尔动力系统相关的C*-代数的代数类似物，这与图C*-代数和Leavitt路径代数之间的关系相平行。 我们证明此类代数是Cuntz-Pimsner代数和部分斜群环，并利用这些事实证明一个分次唯一性定理。 然后我们描述相对广义布尔动力系统的概念，并将分次唯一性定理推广到相对广义布尔动力系统代数。 我们使用分次唯一性定理，以底层动力系统来表征相对广义布尔动力系统代数的分次理想。 我们证明每个广义布尔动力系统代数都与一个没有奇点的广义布尔动力系统相关的代数是Morita等价的。 最后，我们给出一个替代性表征，用于表征广义布尔动力系统代数的类，该表征使用了从Stone对偶性中得出的底层图结构。 显示英文摘要

摘要： We study an algebraic analog of a C*-algebra associated to a generalized Boolean dynamical system which parallels the relation between graph C*-algebras and Leavitt path algebras. We prove that such algebras are Cuntz-Pimsner algebras and partial skew group rings and use these facts to prove a graded uniqueness theorem. We then describe the notion of a relative generalized Boolean dynamical system and generalize the graded uniqueness theorem to relative generalized Boolean dynamical system algebras. We use the graded uniqueness theorem to characterize the graded ideals of a relative generalized Boolean dynamical system algebra in terms of the underlying dynamical system. We prove that every generalized Boolean dynamical system algebra is Morita equivalent to an algebra associated to a generalized Boolean dynamical system with no singularities. Finally, we give an alternate characterization of the class of generalized Boolean dynamical system algebras that uses an underlying graph structure derived from Stone duality.