Twisted Dual-Group Algebras: Equivariant Deformations of C0(G)

We consider a family of twisted Fourier algebras A(G, ω) of a locally compact group G, which in the case of a abelian group G are the Fourier transforms of the usual twisted group algebras of ($) over cap Gô. The corresponding C*-algebras C*(Gô, ω) are deformations of C0(G), which are equivariant in the sense that G still acts by left translation. The main examples come from cocycles σ on the dual of an abelian subgroup H of G; we prove that for such cocycles the twisted dual-group algebras C*(Gô, ω) are induced from the twisted group algebras C*(Hô, σ), and we give detailed formulas for the multiplication on A(G, ω) which extend to larger dense subalgebras of C0(G) and Cb(G). We anticipate that these larger subalgebras will be useful for constructing deformations of homogeneous spaces C0(G/Γ).