Abstract
SupposeGis a group. We equip the groupGwith a cyclic order in such a way so thatP(G), the positive cone under the cyclic order ofGis a semigroup.We construct a representation of the semigroupP(G) as isometries acting on a certainHilbert space.
Highlights
A cyclic order on a group (GG, +) is a ternary relation on GG satisfying some conditions
Given a group (GG, +), and a cyclic order RR on GG which is compatible with the operation on GG, the pair (GG, +, RR) is called as a cyclically ordered group
Given any linearly ordered group (GG, +,
Summary
A cyclic order on a group (GG, +) is a ternary relation on GG satisfying some conditions. The positive cone HH+ of HH is a semigroup, which is linearly ordered under the same order
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