Virasoro-type algebras associated with a Penrose tiling

Abstract

A family of infinite-dimensional Lie algebras with generators in a one-to-one correspondence with the points of a Penrose tiling is introduced. Central extensions, leading to Virasoro-type algebras, are constructed, and highest weight representations for these algebras are considered. Furthermore, extensions to a super-symmetric setting and thus aperiodic analogues to Virasoro super-algebras are discussed.