The socle of subshift algebras, with applications to subshift conjugacy
arxiv(2024)
摘要
We introduce the concept of "irrational paths" for a given subshift and use
it to characterize all minimal left ideals in the associated unital subshift
algebra. Consequently, we characterize the socle as the sum of the ideals
generated by irrational paths. Proceeding, we construct a graph such that the
Leavitt path algebra of this graph is graded isomorphic to the socle. This
realization allows us to show that the graded structure of the socle serves as
an invariant for the conjugacy of Ott-Tomforde-Willis subshifts and for the
isometric conjugacy of subshifts constructed with the product topology.
Additionally, we establish that the socle of the unital subshift algebra is
contained in the socle of the corresponding unital subshift C*-algebra.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要