Invariant Basis Property and the Ideal Structure of Leavitt Path Algebras

Müge Kanuni, Düzce University.
Date: 14th of February, 2018, Wednesday. Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: A ring R is said to have Invariant Basis Number property, or more simply IBN, in case no two free left R-modules of different rank are isomorphic. W. G. Leavitt constructed some non-IBN algebras — what we now call Leavitt algebras — in the 1960’s. The Leavitt path algebra of a quiver with one vertex and m loops turns out to be Leavitt algebra R of type (1,m), that is a non-IBN algebra where R is isomorphic to m-copies of R as a left module and not isomorphic to n-copies of R for any 1 < n < m. On the other hand, there is an abundance of examples of Leavitt path algebras which have IBN. Moreover, we give an algorithm to decide whether a Leavitt path algebra has IBN or not. If time permits, we discuss the ideal structure of Leavitt path algebras.