TWISTED DUAL-GROUP ALGEBRAS - EQUIVARIANT DEFORMATIONS OF C-0(G)

We consider a family of twisted Fourier algebras A(G, omega) 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 ($) over cap G. The corresponding C*-algebras C*(($) over cap G, omega) are deformations of C-o(G), which are equivariant in the sense that G still acts by left translation. The main examples come from cocycles sigma on the dual of an abelian subgroup H of G; we prove that for such cocycles the twisted dual-group algebras C*(($) over cap G, omega) are induced from the twisted group algebras C*(($) over cap H, sigma), and we give detailed formulas for the multiplication on A(G, omega) which extend to larger dense subalgebras of C-o(G) and C-b(G). We anticipate that these larger subalgebras will be used for constructing deformations of homogeneous spaces C-o(G/T). (C) 1995 Academic Press, Inc.