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- W1597555816 abstract "AbstractFor an inclusion of the form (mathbb{C} subseteq M_n (mathbb{C})), where M n (ℂ) is endowed with a state with diagonal weights λ = (λ1, …, λn), we use Popa’s construction, for non-tracial states, to obtain an irreducible inclusion of II1 factors, (N^lambda (Q) subseteq M^lambda (Q)) of index (sum tfrac{1} {{lambda _i }}). Mλ(Q) is identified with a subfactor inside the centralizer algebra of the canonical free product state on Q ⋆ M N (ℂ). Its structure is described by “infinite” semicircular elements as in {xc[32]}.The irreducible subfactor inclusions obtained by this method are similar to the first irreducible subfactor inclusions, of index in [{xc4},∞) constructed in {xc[24]}, starting with the Jones’ subfactors inclusion (R^s subseteq R), s gt; 4. In the present paper, since the inclusion we start with has a simpler structure, it is easier to control the algebra structure of the subfactor inclusions.If the weights correspond to a unitary, finite-dimensional representation of a Woronowicz’s compact quantum group G, then the factor Mλ(Q) is contained in the fixed point algebra of an action of the quantum group on Q ⋆ MN(ℂ), with equality if G is SUq(N), (or SOq(3) when N = 2). By Takesaki duality, the factor Mλ(L(FN)) is Morita equivalent to (mathcal{L})(F∞).This method gives also another approach to find, as also recently proved in {xc[36]}, irreducible subfactors of (mathcal{L})(F∞) for index values bigger than 4.KeywordsSubfactorNon-tracial stateSemicircular element" @default.
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- W1597555816 date "2005-06-27" @default.
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- W1597555816 title "Irreducible Subfactors Derived from Popa’s Construction for Non-Tracial States" @default.
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- W1597555816 doi "https://doi.org/10.1007/3-7643-7314-8_14" @default.
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