Uncountable Abelian Group C*-algebras Fail the Lifting Property

2026/07/22 by Miles Gould
#math.OA

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Abstract

In this note, we show that C^*(G) fails the lifting property (LP) for every discrete group G containing an uncountable abelian subgroup. Consequently, for every uncountable discrete abelian group G, the nuclear algebra C^*(G) has the local lifting property (LLP) but fails the LP. This shows that the LP and the LLP do not coincide for full discrete group C^*-algebras.

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