Lie algebras associated with one-dimensional aperiodic point sets

Details Lie algebras associated with one-dimensional aperiodic point sets Lie algebras associated with one-dimensional aperiodic point sets

2005-07-29

arxiv.org/abs/math-ph/0507072v2

J.Phys.A39:1367-1374,2006

Physics

Mathematical Physics

13 pages

Scientific paper

10.1088/0305-4470/39/6/010

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.

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