Special Lie algebras for quasicrystals

A new type of infinite-dimensional Lie algebra, called aperiodic Virasoro algebra is presented which is by construction compatible with the structure of cut-and-project quasicrystals. The properties of the algebra depend on the acceptance window and thus on the structure of the cut-and-project quasicrystal, and its generators are in a one-to-one correspondence with the points of the latter. By construction, there is a formal resemblance between the aperiodic Virasoro algebra and the usual Virasoro algebra, but due to the influence of the acceptance window, the corresponding properties differ crucially and thus the aperiodic Virasoro algebra is indeed a new algebraic structure. (C) 2000 Elsevier Science B.V. All rights reserved.