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2023-11-13
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How to Cite
ON IRREDUCIBLE HYPERFINITE REAL SUBFACTORS
Kh.Boltayev
Department of General Mathematics, Tashkent state pedagogical University named after Nizami, Tashkent, Uzbekistan.
Z.Hamroqulova
Department of General Mathematics, Tashkent state pedagogical University named after Nizami, Tashkent, Uzbekistan.
Keywords: Hyperfinite factor, W*-algebra, irreducible hyperfinite real subfactors, complex Hilbert space, commutant, coupling constant, involutive *-antiautomorphism, principal graphs.
Abstract
It is shown any hyperfinite factor has an involutive *-antiautomorphism. It is proved that a real subfactor is irreducible if and only if its enveloping factor is irreducible. Using constructed examples in the complex case, as well as using an involutive *-antiautomorphism of a W*-algebra, examples of irreducible hyperfinite real subfactors with index larger than 4 are constructed.
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