Abstract
We consider the group ℤƗlex ℤ as a linear ordered abelian group, and we induce a cyclic order so that the group is cyclically ordered, and denote it as ℤƗCOG ℤ. Suppose σ is a 2-cocycle on the group ℤƗCOG ℤ. We construct an isometric representation of the semigroup (ℤƗCOG ℤ). This representation generates a canonical algebra which we call the twisted Toeplitz algebra of the cyclically ordered group ℤƗCOG ℤ.
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