University of Sydney Algebra Seminar

Madeline Nurcombe

Friday 1 May, 12-1pm, in Carslaw 175

Presentations for the ghost algebra and the label algebra

The ghost algebra is a two-boundary extension of the Temperley-Lieb algebra, constructed recently via a diagrammatic presentation. The existing two-boundary Temperley-Lieb algebra has a basis of two-boundary string diagrams, where the number of strings connected to each boundary must be even. The ghost algebra is similar, but allows this number to be odd, using bookkeeping dots called ghosts to assign a consistent parity to each string endpoint on each boundary. Alternatively, one can obtain an isomorphic algebra by simply labelling these string endpoints with their parities. The resulting algebra may be further generalised to admit any number of labels, instead of just "even" and "odd"; we call this the label algebra, and establish a non-diagrammatic presentation for it, from which a presentation for the ghost algebra may be deduced.