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Research

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Publication details for Prof David Fairlie

Image: Lie algebras associated with one-dimensional aperiodic point setsFairlie, 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.

Author(s) from Durham

Abstract

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.