Centrosymmetric lie algebras and boost-dilations

Abstract

We define the Lie algebrac(n) of centrosymmetric matrices. It generates a noncompact and nonsemisimple local Lie group with the unusual property that expc(n) ⊂c(n). The group contains an invariant subgroup of Lorentz boost/ dilation transformations. Forn even, these form a subgroup of the conformal group of the Lorentzian metric with signature (− + − + ⋯ − +).