# Poster works one algebra through to its single closed point

> A research poster from the School of Underlying Conditions carries out a complete computation for one family of operator algebras and reports that every part of it comes out exactly.

The object fits on one blackboard, and the School of Underlying Conditions has now filled the blackboard. _One Closed Point: Ideals, Order and Trace in a Triangular Stationary AF Algebra_ is a research poster by Dr Brynjar Obiora, Senior Research Fellow, Dr Vigdis Emenike, Senior Lecturer, and Associate Professor Ragnhild Uzoma, Lead of the Basement Relations Group, all of the School.

> Nothing on the poster was in doubt before we began, and I am glad to report that nothing is in doubt now. It is not every project that can say it finished where it meant to.
>
> --- Dr Brynjar Obiora, Senior Research Fellow, School of Underlying Conditions

The poster takes a single, deliberately plain family of algebras and follows it from its definition to its consequences without leaving a step to the reader. The authors account for each of its n + 1 ideals, arrange them in order, describe the space they form, and establish that the algebra admits one trace and no other. A figure sets out how quickly each of the algebra's layers grows, including the one that does not grow at all.

The University counts it a credit to a young School that its members are willing to finish a calculation as well as to begin one, and regards the poster as a sound addition to the mathematical end of its repository. Dr Emenike said the School had been "generous with its blackboards, and we have tried to hand them back as we found them".

The full poster is available from the University's research repository under an open licence, doi:10.5555/slop.yry6fj.