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Three Fibonacci-Chain aperiodic algebras
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Orientador(es)
Resumo(s)
Aperiodic algebras are infinite dimensional algebras with generators
corresponding to an element of the aperiodic set. These algebras proved to be
an useful tool in studying elementary excitations that can propagate in
multilayered structures and in the construction of some integrable models in
quantum mechanics. Starting from the works of Patera and Twarock we present
three aperiodic algebras based on Fibonacci-chain quasicrystals: a quasicrystal
Lie algebra, an aperiodic Witt algebra and, finally, an aperiodic Jordan
algebra. While a quasicrystal Lie algebra was already constructed from a
modification of the Fibonacci chain, we here present an aperiodic algebra that
matches exactly the original quasicrystal. Moreover, this is the first time to
our knowledge, that an aperiodic Jordan algebra is presented leaving room for
both theoretical and applicative developments.
Descrição
Palavras-chave
Aperiodic algebras Fibonacci chain Jordan algebras Lie algebras
Contexto Educativo
Citação
Editora
Taylor & Francis