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Cayley Compactifications of Abelian Groups
Mike Develin
Department of Mathematics, University of California, Berkeley, CA 94720-3840, USA
Annals of Combinatorics 6 (3) p.295-312 September, 2002
AMS Subject Classification: 52B20, 52C99, 20F99
Following work of Rieffel [1], we define the Cayley compactification of a discrete Abelian group G with a distinguished finite set of generators S. We use algebraic methods in the general case to construct an explicit presentation of Cayley compactifications. In the particular case of , we use geometric methods to demonstrate a strong and explicit connection between the Cayley compactification and the polytope polar to .
Keywords: Cayley graph, Cayley compactification


1. M.A. Rieffel, Group C*-algebras as compact quantum metric spaces, Doc. Math. 7 (2002) 605ĘC651.

2. B. Sturmfels, N. Trung, and W. Vogel, Bounds on degrees of projective schemes, Math. Ann. 302 (1995) 417ĘC432.