Jones, V. F. R. Index for subfactors. (English) Zbl 0508.46040 Invent. Math. 72, 1-25 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 47 ReviewsCited in 625 Documents MSC: 46L10 General theory of von Neumann algebras 46L35 Classifications of \(C^*\)-algebras 46L40 Automorphisms of selfadjoint operator algebras Keywords:index of a subfactor; coupling constants; conditional expectations; Bratteli diagrams; relative commutant PDFBibTeX XMLCite \textit{V. F. R. Jones}, Invent. Math. 72, 1--25 (1983; Zbl 0508.46040) Full Text: DOI EuDML References: [1] Aubert, P.L.: Théorie de Galois pour uneW *-algèbre. Comment. Math. Helv.39, 411-433 (1976) · Zbl 0339.46044 · doi:10.1007/BF02568166 [2] Baker, B., Powers, R.: Product states andC * dynamical systems of product type. Preprint, University of Pennsylvania [3] Bourbaki, N.: Algèbre, Ch. 8. Hermann 1959. · Zbl 0102.25503 [4] Bratteli, O.: Inductive limits of finite dimensionalC *-algebras. Trans. A.M.S.171, 195-234 (1972) · Zbl 0264.46057 [5] Christensen, E.: Subalgebras of a finite algebra. Math. Ann.243, 17-29 (1979) · doi:10.1007/BF01420203 [6] Connes, A.: Periodic automorphisms of the hyperfinite factor of type II1. Acta Sci. Math.39, 39-66 (1977) · Zbl 0382.46027 [7] Connes, A.: Classification of injective factors. Ann. Math.104, 73-115 (1976) · Zbl 0343.46042 · doi:10.2307/1971057 [8] Connes, A.: Sur la théorie non-commutative de l’intégration. In: Algèbres d’opérateurs. Lecture Notes in Mathematics, Vol. 725 Berlin-Heidelberg-New York: Springer 1978 [9] Connes, A.: A II1 factor with countable fundamental group. J. Operator Theory4, 151-153 (1980) · Zbl 0455.46056 [10] Dixmier, J.: Les algèbres d’opérateurs dans l’espace Hilbertien. Deuxieme édition. Ganthier Villars, 1969 [11] Effros, E., Shen, C.-L.:A-F C *-algebras and continued fractions. Indiana Math. J.29, 191-204 (1980) · Zbl 0457.46046 · doi:10.1512/iumj.1980.29.29013 [12] Enomotor, M., Watatani, Y.:C *(?) and Cuntz algebras from Young diagrams. Preprint [13] Feller, W.: Probability theory and its applications. I. Wiley and Sons, Inc. 1957 · Zbl 0077.12201 [14] Goldman, M.: On subfactors of factors of type II1. Mich. Math. J.7, 167-172 (1960) · Zbl 0121.10002 [15] Handelman, D.: Notes on orderedK-theory. Vancouver conference on operator algebras (1982) [16] Husemoller, D.: Fibre bundles. Grad. Texts in Math. Vol. 20. Berlin-Heidelberg-New York: Springer 1975 · Zbl 0307.55015 [17] Jones, V.: Sur la conjugaison des sous-facteurs des facteur de type II1. C.R. Ac. Sci. Paris t.286, 597-598 (1977) · Zbl 0344.46128 [18] Jones, V.: L’indice des sous-facteurs de facteurs de type II1. C.R. Ac. Sci. Paris t. 286 (1977), 597-598 · Zbl 0344.46128 [19] Kadison, R., Fugledge, B.: On a conjecture of Murray and von Neumann. Proc. Natl. Acad. Sci. U.S.37, 420-425 (1951) · Zbl 0043.11702 · doi:10.1073/pnas.37.7.420 [20] Murray, F., von Neumann, J.: On rings of operators, II. Trans. A.M.S.41, 208-248 (1937) · Zbl 0017.36001 · doi:10.1090/S0002-9947-1937-1501899-4 [21] Murray, F., von Neumann, J.: On rings of operators, IV. Ann. Math.44 716-808 (1943) · Zbl 0060.26903 · doi:10.2307/1969107 [22] Ocneanu, A.: Actions of discrete amenable groups on factors. To appear, Springer Lecture notes in Math. Berlin-Heidelberg-New York: Springer [23] Popa, S.: On a problem of R.V. Kadison on maximal abelian *-subalgebras in factors. Invent. Math.65, 269-281 (1981) · Zbl 0481.46028 · doi:10.1007/BF01389015 [24] Skau, C.: Finite subalgebras of a von Neumann algebra. J. Funct. Anal.25, 211-235 (1977) · Zbl 0347.46070 · doi:10.1016/0022-1236(77)90068-4 [25] Suzuki, N.: Crossed products of rings of operators. Tohoku Math. J.7, 167-172 (1960) · Zbl 0114.31801 [26] Suzuki, N.: Extensions of rings of operators in Hilbert spaces. Tohoku Math. J.14, 217-232 (1962) · Zbl 0178.16701 · doi:10.2748/tmj/1178244177 [27] Stratila, S., Voiculescu, D.: Representations ofAF algebras and of the groupU(?). Springer Lecture notes in Math. · Zbl 0318.46069 [28] Takesaki, M.: Theory of operator algebras I. Berlin-Heidelberg-New York: Springer 1979 · Zbl 0436.46043 [29] Topping, D.: Lectures on von Neumann algebras. Nostrand Reinhold Math. Studies, 1969 · Zbl 0218.46061 [30] Umegaki, H.: Conditional expectation in an operator algebra I. Tohoku Math. J.6, 358-362 (1954) · Zbl 0058.10503 · doi:10.2748/tmj/1178245177 [31] Wasserman, A.: Thesis, University of Pennsylvania, 1981 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.