Algebra Seminar: Nurcombe -- The ghost algebra and the dilute ghost algebra

Madeline Nurcombe (USyd) will be speaking in the algebra seminar this week.  We will go
out for lunch after the talk.  All are welcome! 

Where: Carslaw 275 

When: Friday 11 October, 12-1pm 

Title: The ghost algebra and the dilute ghost algebra 

Abstract: The Temperley-Lieb (TL) algebra has a wide range of applications, from
physical models of polymers and quantum spin chains, to knot theory.  Its basis elements
can be expressed as rectangular diagrams of non-crossing strings, with multiplication
based on concatenation of diagrams.  There are also one- and two-boundary TL algebras,
describing physical systems with boundaries, but the two-boundary TL algebra requires
its diagrams to have an even number of strings connected to each boundary.  In this
talk, I will introduce the ghost algebra, a two-boundary generalisation of the TL
algebra that allows diagrams with odd or even numbers of strings at each boundary.  Its
diagrams contain ghosts: dots on the boundaries that act as bookkeeping devices to
ensure associativity of multiplication.  I will also introduce the dilute generalisation
of the ghost algebra, and discuss the lattice models associated with these algebras.
(arXiv: 2308.11966)