|Title:||Symbolic dynamics and Leavitt path algebras|
|Speaker:||Roozbeh Hazrat (University of Western Sydney)|
Let A and B be square matrices filled with non-negative integers.
We say that A and B are related if there are two (not necessarily square)
matrices R and Ssuch that A=RS and B=SR. We say two square matrices
are s-related if there is a chain of related matrices connecting them.
Given two matrices, it is not known how to find out if they are s-related.
The s-relation between matrices (which is formally called strong shift
equivalent!) appears in the classification theory of symbolic dynamics on
one hand and the subject of Leavitt path algebras (certain algebras
associated to graphs) on the other hand.
In this talk we introduce the graded Grothendieck group, grK0 and show how this invariant is connected to s-related matrices. We then discuss how (conjecturally) graded K-theory could relate these two subjects and play the role of a complete invariant for the classification.