C$^*$-algebras from planar algebras I: Canonical C$^*$-algebras associated to a planar algebra
نویسندگان
چکیده
منابع مشابه
A 2 -planar Algebras I
We give a diagrammatic representation of the A2-Temperley-Lieb algebra, and show that it is isomorphic to Wenzl’s representation of a Hecke algebra. Generalizing Jones’s notion of a planar algebra, we construct an A2-planar algebra which will capture the structure contained in the SU(3) ADE subfactors. We show that the subfactor for an ADE graph with a flat connection has a description as a fla...
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An inclusion of II1 factors N ⊂ M with finite Jones index gives rise to a powerful set of invariants that can be approached successfully in a number of different ways. We describe Jones’ pictorial description of the standard invariant of a subfactor as a so-called planar algebra and show how this point of view leads to new structure results for subfactors. 2000 Mathematics Subject Classificatio...
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In this paper, we show the relation between the Schur algebras Sr Λ,Σ(B) and S r′ Λ,Σ(B), where 1 ≤ r ′ < r < ∞. Then we set up the involution operator in these Schur algebras and show that with this involution operator there is only one C∗-algebra among these classes of Banach algebras. Furthermore, we show the equivalence of a condition on the Schur multiplier norm and the existence of C∗-alg...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2016
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6781