Abstract
We consider the C*-subalgebra of the algebra of all bounded operators on Hilbert space of square-summable functions on some countable set. The algebra being investigated is generated by a family of partial isometries. These isometries satisfy the relations defined by a preassigned mapping on the set. It is assumed that the mapping has elements with finite orbits. Under this assumption the algebra we consider contains the subalgebra of compact operators and its quotient algebra is \( \mathbb{Z} \)-graded. We consider the covariant system associated with the quotient algebra and construct the conditional expectation onto the fixed point subalgebra. We prove that the quotient algebra is nuclear and so is the algebra generated by mapping.
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