Research Projects

This pilot project aims to use Lie ideals expertise to prove that weakly central groups provide a dichotomy between two long open problems about C*-algebras. The first problem focuses on finding a projection in C*(G), while the second problem is its antithesis and whether the span of projections is dense in C*(G). The project aims to provide a bigger frame of reference to these problems and enhance the possibilities of using diverse techniques. G is considered weakly central if C*(G) is a weakly central C*-algebra and G e [WC]. To reach a conclusion on the conjectures, one must focus on those groups not weakly central. To answer the second question, one must pay attention to only the weakly central groups. The project aims to answer two major problems for full group C*-algebras and possibly other algebras related to groups. It is ambitious as it proposes to study long-open problems from a new perspective, but the proposed methodology makes the goals achievable. Realizing these goals within two years will require perseverance, hard work, and periodic discussions with Prof. Prahlad Vaidyanathan. Note that this project does not concern group von Neumann algebras, as their Dixmier property implies they are weakly central.