论文标题
图形和超级图的莫里塔等效性莱维特路径代数
Morita Equivalence of Graph and Ultragraph Leavitt Path Algebras
论文作者
论文摘要
本论文的主要目的是表明每一个超级莱维特路径代数是莫里塔等效的，作为一个环，与图形leavitt路径代数相当。 Takeshi Katsura，Paul Muhly，Aidan Sims和Mark Tomforde显示了每一个Ultragraph $ C^{*} $ - 代数是Morita等效的，在$ C^{*} $ - sense中，sense-sence-sense，sense，向图$ c^{*} $ - algebra;我们的结果是这一事实的代数类似物。此外，我们将利用结果为既定条件提供了替代证明，以确保超级莱维特路径代数在字段上的简单性。
The primary purpose of this thesis is to show every ultragraph Leavitt path algebra is Morita equivalent, as a ring, to a graph Leavitt path algebra. Takeshi Katsura, Paul Muhly, Aidan Sims, and Mark Tomforde showed every ultragraph $C^{*}$-algebra is Morita equivalent, in the $C^{*}$-sense, to a graph $C^{*}$-algebra; our result is an algebraic analog of this fact. Further, we will use our result to give an alternate proof for established conditions which guarantee the simplicity of an ultragraph Leavitt path algebra over a field.
