Algebra Seminar: Nurcombe -- Presentations for the ghost algebra and the label algebra

Madeline Nurcombe (University of Sydney) will be speaking in the algebra seminar.  We
will go out for lunch after the talk---all are welcome to join! 

When: 12-1pm Friday May 1st 

Where: Carslaw 175 

Title: Presentations for the ghost algebra and the label algebra 

Abstract: 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.