WEEKLY ACTIVITIES

Time: 9h, Wednesday, May 20, 2020
Online via google meet: https://meet.google.com/vha-ujbp-kwo

Abstract: A current program in the theory of Leavitt path algebras is to classify the Leavitt path algebras up to Morita equivalence in terms of an invariant that can be easily calculated from the graph. This question has been investigated in numerous articles. In large part this research effort has been motivated by the goal of resolving the Morita equivalence conjecture. Since Morita equivalence passes to corners, it may be germane to the resolution of the Morita equivalence conjecture to understand situations in which a corner of a Leavitt path algebra is again a Leavitt path algebra, or at least Morita equivalent to a Leavitt path algebra. It is well-known that any corner of the Leavitt path algebra of a finite graph is isomorphic to another Leavitt path algebra. This result notwithstanding, it turns out that a corner of the Leavitt path algebra of an arbitrary graph need not in general be isomorphic to a Leavitt path algebra. In this talk, we show that every corner of such Leavitt path algebras is in fact isomorphic to an algebra of a more general type, to wit, a Steinberg algebra. This is joint work with Gene Abrams and Mikhailo Dokuchaev.