Operator Algebra seminar

Speaker:  Scott Schmieding (University of Maryland)

Title: Strong shift equivalence of matrices over a ring

Abstract: Over a ring R, two square matrices A, B are elementary strong shift equivalent over R (ESSE-R) if there are matrices U,V over R such that A=UV and B = VU. Strong shift equivalence over R (SSE-R) is the equivalence relation generated by ESSE-R. Shift equivalence over R (SE-R) is a more manageable equivalence relation which is refined by SSE-R. We consider the question: when does SE-R imply SSE-R? We discuss how the refinement of SE-R by SSE-R is captured by a quotient of the group NK₁(R) of algebraic K-theory. For many rings (but not all), it follows that SE-R and SSE-R are equivalent. We mention some applications, including resolution of a question of Parry regarding group extensions of shifts of finite type.

How to find Room 4-0-10: Enter the Biocenter through the entrance at the construction site. Turn right where you usually turn left to go to the canteen, and follow the signs to building 4. The seminar room is down the corridor on the right hand side.