Publication details for Prof David FairlieFairlie, David B., Twarock, Reidun & Zachos, Cosmas K. (2006). Lie algebras associated with one-dimensional aperiodic point sets. Journal of Physics A 39(2): 1367-1374.
- Publication type: Journal papers: academic
- ISSN/ISBN: 0305-4470 (print), 1361-6447(online)
- View online: Online version
Author(s) from Durham
The set of points of a one-dimensional cut-and-project quasicrystal or model set, while
not additive, is shown to be multiplicative for appropriate choices of
acceptance windows. This leads to the definition of an associative additive graded composition
law and permits the introduction of Lie algebras over such aperiodic point sets. These infinite dimensional Lie algebras are shown to be representatives of a new type of semi-direct product induced Lie algebras.