University of Sydney Algebra Seminar
Madeline Nurcombe
Friday 11 October, 12-1pm, Place: Carslaw 275
The ghost algebra and the dilute ghost algebra
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)