Cayley Compactifications of Abelian Groups

Mike Develin

Department of Mathematics, University of California, Berkeley, CA 94720-3840, USA

develin@math.berkeley.edu

Annals of Combinatorics 6 (3) p.295-312 September, 2002

Abstract:

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 .

References:

1. M.A. Rieffel, Group C*-algebras as compact quantum metric spaces, Doc. Math. 7 (2002) 605¨C651.

2. B. Sturmfels, N. Trung, and W. Vogel, Bounds on degrees of projective schemes, Math. Ann. 302 (1995) 417¨C432.