Algebra Seminar | On Modules that Witness that Certain Leavitt Path Algebras are Directly Infinite, April 6

The Algebra Seminar features Dr. Nicholas Pilewski on Thursday, April 6, from 4:30-5:30 pm. in Morton 313.

Pilewski, a lecturer in Mathematics at Ohio University, will present “On modules that witness that certain Leavitt Path Algebras are directly infinite.” He is also an alum, earning an M.S. and Ph.D. in Mathematics from the College of Arts & Sciences.

Abstract: A ring $R$ is said to be \textit{directly infinite} when there exists a right $R$-module $B \neq 0$ such that $R \cong R \oplus B$ as a right $R$-module. In terms of the abelian monoid $V(R)$ of isomorphism classes of finitely generated projective right $R$-modules, $R$ is directly infinite when there exists a finitely generated projective $R$-module $B \neq 0$ such that $[R] = [R] + [B]$ in $V(R).$ Given a graph $E,$ we completely identify in terms of the graph $E$ all those finitely generated projective right $L_K(E)$-modules $B$ for which $[L_K(E)] = [L_K(E)] + [B]$ in $V(L_K(E)).$ (joint work with Sergio R. Lopez-Permouth.)