Title: Leavitt Path Algebras with Bases Consisting Solely of Units
Speaker: Nick Pilewski, Ohio University
Seminar Type: OSU-OU Ring Theory Seminar
Abstract: Following López-Permouth, Moore and Szabo, given a ring \(R\), an \(R\)-algebra \(A\) is called an invertible algebra if it has an \(R\)-basis of units in \(A\). Leavitt path algebras are generalizations of the classical Leavitt algebras, the universal examples of algebras without the Invariant Basis Number property. In this talk, we report on the search for a condition on the graph \(E\) which is equivalent to the Leavitt path algebra \(L_K(E)\) being an invertible algebra for any field \(K \neq \mathbb{F}_2\). Leavitt path algebras with coefficients in \(\mathbb{F}_2\) and commutative rings are also considered. (This is a joint work with Sergio López-Permouth.)
