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Strongly irreducible operators, K0-groups, and Jones indices in the hyperfinite type II1 factor

  • Junsheng Fang
  • Chunlan Jiang
  • Minghui Ma
  • Rui Shi
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Abstract

In this paper, we study the strong irreducibility of a class of operators associated with irrational rotation algebras in the hyperfinite type II1 factor ℛ. By developing weighted shift models for their relative commutants, we obtain K0 calculations and splitting criteria for direct sums. In particular, we construct strongly irreducible operators in ℛ whose relative commutants have K0-groups isomorphic to ℤ and ℤ2. We realize every Jones index of an irreducible subfactor of ℛ as [ℛ:W*(T)] for some strongly irreducible operator T relative to ℛ. Furthermore, we construct strong generators of ℛ and strongly irreducible operators in every type II1 factor ℳ with separable predual.

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Cite

BibTeXRIS
BibTeX
@misc{fang2026strongly,
  title = {{Strongly irreducible operators, $K_0$-groups, and Jones indices in the hyperfinite type $\mathrmII_1$ factor}},
  author = {Junsheng Fang and Chunlan Jiang and Minghui Ma and Rui Shi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22028},
  eprint = {2610.22028},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22028},
}
RIS
TY  - UNPB
TI  - Strongly irreducible operators, K_0-groups, and Jones indices in the hyperfinite type II_1 factor
AU  - Junsheng Fang
AU  - Chunlan Jiang
AU  - Minghui Ma
AU  - Rui Shi
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22028
UR  - https://arxiv.org/abs/2610.22028
AB  - In this paper, we study the strong irreducibility of a class of operators associated with irrational rotation algebras in the hyperfinite type II_1 factor ℛ. By developing weighted shift models for their relative commutants, we obtain K_0 calculations and splitting criteria for direct sums. In particular, we construct strongly irreducible operators in ℛ whose relative commutants have K_0-groups isomorphic to ℤ and ℤ^2. We realize every Jones index of an irreducible subfactor of ℛ as [ℛ:W^*(T)] for some strongly irreducible operator T relative to ℛ. Furthermore, we construct strong generators of ℛ and strongly irreducible operators in every type II_1 factor ℳ with separable predual.
ER  -