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Strongly irreducible operators, $K_0$-groups, and Jones indices in the hyperfinite type $\mathrm{II}_1$ factor
In this paper, we study the strong irreducibility of a class of operators associated with irrational rotation algebras in the hyperfinite type $\mathrm{II}_1$ factor $\mathcal R$. By developing weighted shift models for their relative commutants, we obtain $K_0$ calculations and splitting criteria f
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