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

We consider a family of twisted Fourier algebras A(G, omega) of a loca lly compact group G, which in the case of a abelian group G are the Fo urier transforms of the usual twisted group algebras of ($) over cap G . The corresponding C-algebras C*(($) over cap G, omega) are deformat ions of C-o(G), which are equivariant in the sense that G still acts b y 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 th e twisted dual-group algebras C(($) over cap G, omega) are induced fr om the twisted group algebras C(($) over cap H, sigma), and we give d etailed 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 the se larger subalgebras will be used for constructing deformations of ho mogeneous spaces C-o(G/T). (C) 1995 Academic Press, Inc.