Algebraic geometry of crossed products

Abstract

For projective variety X we introduce a C*-algebra A_X defined as the norm-closure of representation of the twisted homogeneous coordinate ring of X by the linear operators on a Hilbert space H. Our main result says that points of X are bijective with the irreducible representations of crossed product of A_X by certain automorphism of A_X; the proof is based on the Takai duality for crossed products. We illustrate the theorem by an example of A_X being the so-called noncommutative torus with real multiplication.Comment: 14 pages; improved expositio