三个Fibonacci链非周期代数
Three Fibonacci-Chain Aperiodic Algebras
摘要：
非周期代数是无限维代数，其生成元对应于非周期集合的元素。这些代数被证明是一个有用的工具，在研究基本激发，可以在多层结构中传播，并在量子力学中的一些可积模型的建设。从Patera和Twarock的工作出发，我们给出了三个基于Fibonacci链准晶的非周期代数：准晶李代数，非周期Witt代数，最后是非周期Jordan代数.虽然准晶体李代数已经从斐波纳契链的修改，我们在这里提出了一个非周期代数，完全匹配原来的准晶体。此外，这是第一次，我们的知识，提出了一个非周期的约旦代数留下的空间，理论和应用的发展。
英文摘要：
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.
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