Ring Theory Seminar | Diagonal Preserving Ring *-isomorphisms of Leavitt Path Algebas, March 18

The Ohio University-Ohio State University Ring Theory Seminar presents Dr. Jonathon Brown on “Diagonal preserving ring *-isomorphisms of Leavitt path algebas” on Friday, March 18,  at 4:45-5:45 p.m. in Cockins Hall 240, OSU-Columbus.

Brown is Assistant Professor of Mathematics at the University of Dayton.

Abstract: Abrams and Tomforde conjectured that the Leavitt Path algebra over the complex numbers of two graphs are isomorphic as rings implies the corresponding C*-algebras are isomorphic.  In this talk I present joint work with Clark and an Huef that provides partial progress to answering this conjecture:   we show that if E and F are graphs with L(E) isomorphic to L(F) as *-rings by an isomorphism that preserves the diagonal then C*(E) is isomorphic to C*(F).   To prove this theorem we use groupoid methods inspired by the work of Brownlowe, Carlsen and Whittaker that shows that C*(E) is congruent to  C*(F)  by a diagonal preserving isomorphism if and only if their graph groupoids are.  We show this theorem using different methods for *-ring isomorphic Leavitt path algebras over integral domains. Since isomorphic groupoids give isomorphic C*-algebras this provides the progress towards the Abrams-Tomforde conjecture.