Abstract
Let A A be a unital Banach algebra and G \mathcal {G} the group of isometries in A A . The norm in A A is uniquely maximal if G \mathcal {G} is not contained in any larger bounded group in A A and there is no equivalent norm on A A with the same group of isometries. We use a group theory result of B. H. Neumann to prove that the discrete measure algebra l 1 ( G ) {l^1}(G) is uniquely maximal if and only if G G has no finite conjugacy classes.
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