Abstract
LetG be a locally compact group with polynomial growth and symmetricL1-algebra andN a closed normal subgroup ofG. LetF be a closedG-invariant subset of Prim*L1(N) andE={kerπ;π∈Ĝ with π|N(k(F))=0}. We prove thatE is a spectral subset of Prim*L1(G) ifF is spectral. Moreover we give the following application to the ideal theory ofL1(G). Suppose that, in addition,N is CCR andG/N is compact. Then all primary ideals inL1(G) are maximal, provided allG-orbits in Prim*L1(N) are spectral.
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