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Lie algebras associated with one-dimensional aperiodic point sets

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JournalJournal of Physics A: Mathematical and General
DatePublished - 10 Feb 2006
Issue number6
Number of pages8
Pages (from-to)1367-1374
Original languageEnglish


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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