Time: 9h, Wednesday, June 24, 2020

Location: Room 612, Building A6, Institutte of Mathematics and GM https://meet.google.com/vha-ujbp-kwo

Abstract: In this talk, we identify the fields $K$ and Hausdorff ample groupoids $mathcal{G}$ for which the simple Steinberg algebra $A_K(mathcal{G})$ yields a simple Lie algebra $[A_K(mathcal{G}), A_K(mathcal{G})]$. We apply the obtained results on simple Leavitt path algebras, simple Kumjian-Pask algebras and simple Exel-Pardo algebras to determine their associated Lie algebras are simple. In particular, we provide easily computable criteria to determine which Lie algebras of the form $[L_K(E), L_K(E)]$ are simple, when $E$ is an arbitrary graph and the Leavitt path algebra $L_K(E)$ is simple.