"Projections in the l1 algebra of a crystal group: an example"
Carline, EmmaA crystal group is a discrete group consisting of the symmetries of a crystal. For such a group G there is a Fourier-like transform F that identifies the algebra l1(G) with a matrix algebra whose entries are functions in the Wiener algebra of the torus. The projections in l1(G) are defined to be the self-adjoint idempotents. A well known collection of these are the sums of point masses over a finite subgroup of G. But are there other kinds of projections? For the 2-dimensional crystal group p2, we characterize projections in F(l1(p2)) and use this to construct projections in l1(p2) with interesting properties and which do not come from a finite subgroup.