Toeplitz Algebras of Cyclically Ordered Groups
Isnie Yusnitha, Rizky Rosjanuardi, Sumanang Muhtar Gozali
Department of Mathematics Education, Universitas Pendidikan Indonesia
Abstract
Suppose G is a cyclically ordered group. In general, a positive cone P(G) is not necessarily a semigroup. Nevertheless, for particular class of cyclically ordered group G, namely linear cyclically ordered group, P(G) is a semigroup. Furthermore, one can verify that the semigroup P(G) admits a representation on a Hilbert space. We develop the classical Toeplitz algebra theory to more general setting of ordered group, that is, to each cyclically ordered group G such that the positive cone P(G) is a semigroup, we define a Toeplitz algebra Τ (G).
Keywords: cyclically ordered group, linear, semigroup, Toeplitz algebras
Topic: Mathematics