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FRAÏSSÉ LIMITS OF C*-ALGEBRAS

  • CHRISTOPHER J. EAGLE (a1), ILIJAS FARAH (a2) (a3), BRADD HART (a4), BORIS KADETS (a5), VLADYSLAV KALASHNYK (a6) and MARTINO LUPINI (a7)...

Abstract

We realize the Jiang-Su algebra, all UHF algebras, and the hyperfinite II1 factor as Fraïssé limits of suitable classes of structures. Moreover by means of Fraïssé theory we provide new examples of AF algebras with strong homogeneity properties. As a consequence of our analysis we deduce Ramsey-theoretic results about the class of full-matrix algebras.

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[1] Ben Yaacov, I., Fraïssé limits of metric structures, this Journal, vol. 80 (2015), no. 1, pp. 100115.
[2] Ben Yaacov, I., Berenstein, A., Henson, C. W., and Usvyatsov, A., Model theory for metric structures , Model Theory with Applications to Algebra and Analysis, Vol. II (Chatzidakis, Z. et al. , editors), London Mathematical Society Lecture Note Series, vol. 350, Cambridge University Press, Cambridge, 2008, pp. 315427.
[3] Blackadar, B., Operator algebras , Encyclopaedia of Mathematical Sciences, vol. 122, Springer-Verlag, Berlin, 2006.
[4] Davidson, K., C*-Algebras by Example, American Mathematical Society, Providence, RI, 1996.
[5] Eagle, C. J., Farah, I., Kirchberg, E., and Vignati, A., Quantifier elimination in C*-algebras, (2015). arXiv:1502.00573.
[6] Eagle, C. J., Goldbring, I., and Vignati, A., The pseudoarc is a co-existentially closed continuum, (2015). arXiv:1503.03443.
[7] Eagle, C. J. and Vignati, A., Saturation and elementary equivalence of C*-algebras . Journal of Functional Analysis, vol. 269 (2015), pp. 26312664.
[8] Elliott, G. A. and Toms, A. S., Regularity properties in the classification program for separable amenable C*-algebras . Bulletin of the American Mathematical Society, vol. 45 (2008), no. 2, pp. 229245.
[9] Farah, I., Logic and operator algebras , Proceedings of the Seoul ICM (Jang, S. Y., Kim, Y. R., Lee, D.-W., and Yie, I., editors), vol. II, Kyung Moon SA, Seoul, 2014, pp. 1540.
[10] Farah, I., Selected applications of logic to classification problem of C*-algebras , E-recursion, Forcing and C*-Algebras (Chong, C. T. et al. , editors), Lecture Note Series, Institute for Mathematical Sciences, National University of Singapore, vol. 27, World Scientific, Singapore, 2014, pp. 182.
[11] Farah, I., Hart, B., Rørdam, M., and Tikuisis, A., Relative commutants of strongly self-absorbing C*-algebras, Selecta Mathematica , to appear.
[12] Farah, I., Hart, B., and Sherman, D., Model theory of operator algebras II: Model theory . Israel Journal of Mathematics, vol. 201 (2014), pp. 477505.
[13] Farah, I., Toms, A. S., and Törnquist, A., Turbulence, orbit equivalence, and the classification of nuclear C*-algebras . Journal für die reine und angewandte Mathematik, vol. 688 (2014), pp. 101146.
[14] Fraïssé, R., Sur l’extension aux relations de quelques propriétés des ordres . Annales Scientifiques de l’École Normale Supérieure. Troisième Série, vol. 71 (1954), pp. 363388.
[15] Giordano, T. and Pestov, V., Some extremely amenable groups . Comptes Rendus Mathematique, vol. 334 (2002), no. 4, pp. 273278.
[16] Glimm, J. G., On a certain class of operator algebras . Transactions of the American Mathematical Society, vol. 95 (1960), no. 2, pp. 318340.
[17] Gromov, M., Filling Riemannian manifolds . Journal of Differential Geometry, vol. 18 (1983), no. 1, pp. 1147.
[18] Hart, B., Goldbring, I., and Sinclair, T., The theory of tracial von Neumann algebras does not have a model companion, this Journal, vol. 78 (2013), no. 3, pp. 10001004.
[19] Jacelon, B., A simple, monotracial, stably projectionless C*-algebra . Journal of the London Mathematical Society, vol. 87 (2013), pp. 365383.
[20] Jiang, X. and Su, H., On a simple unital projectionless C*-algebra . American Journal of Mathematics, vol. 121 (1999), pp. 359413.
[21] Kechris, A. S., Pestov, V., and Todorcevic, S., Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups . Geometric & Functional Analysis GAFA, vol. 15 (2005), no. 1, pp. 106189.
[22] Kirchberg, E., Exact C*-algebras, tensor products, and the classification of purely infinite algebras , Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, , 1994), Birkhäuser, Basel, 1995, pp. 943954.
[23] Kubiś, W. and Solecki, S., A proof of uniqueness of the Gurariĭ space . Israel Journal of Mathematics, vol. 195 (2013), no. 1, pp. 449456.
[24] Lupini, M., Uniqueness, universality, and homogeneity of the noncommutative Gurarij space, (2014). arXiv:1410.3345.
[25] Masumoto, S., Jiang-Su algebra as a Fraïssé limit, (2016). arXiv:1602.00124.
[26] Melleray, J. and Tsankov, T., Extremely amenable groups via continuous logic, (2014). arxiv:1404.4590.
[27] Pestov, V., Dynamics of Infinite-Dimensional Groups, University Lecture Series, vol. 40, American Mathematical Society, Providence, RI, 2006.
[28] Razak, S., On the classification of simple stably projectionless C*-algebras . Canadian Journal of Mathematics, vol. 54 (2002), no. 1, pp. 138224.
[29] Robert, L., Classification of inductive limits of 1-dimensional NCCW complexes . Advances in Mathematics, vol. 231 (2012), no. 5, pp. 28022836.
[30] Rørdam, M., Larsen, F., and Laustsen, N. J., An Introduction to K-Theory for C* Algebras, London Mathematical Society Student Texts, vol. 49, Cambridge University Press, Cambridge, 2000.
[31] Rørdam, M. and Størmer, E., Classification of nuclear C*-algebras. Entropy in operator algebras , Encyclopaedia of Mathematical Sciences, vol. 126, Operator Algebras and Non-commutative Geometry, vol. 7, Springer-Verlag, Berlin, 2002.
[32] Sabok, M., Completeness of the isomorphism problem for separable C*-algebras . Inventiones Mathematicae, (2015), pp.136.
[33] Sato, Y., White, S., and Winter, W., Nuclear dimension and Ƶ-stability . Inventiones Mathematicae, vol. 202 (2015), pp. 893921.
[34] Schochet, C., Topological methods for C*-algebras II: Geometric resolutions and the Künneth formula . Pacific Journal of Mathematics, vol. 98 (1982), pp. 399445.
[35] Schoretsanitis, K., Fraïssé Theory for Metric Structures , Ph.D. thesis, University of Illinois at Urbana-Champaign, 2007.
[36] Thiel, H. and Winter, W., The generator problem for Ƶ-stable C*-algebras . Transactions of the American Mathematical Society, vol. 366 (2014), pp. 23272343.
[37] Toms, A. S. and Winter, W., Strongly self-absorbing C*-algebras . Transactions of the American Mathematical Society, vol. 359 (2007), no. 8, pp. 39994029.

Keywords

FRAÏSSÉ LIMITS OF C*-ALGEBRAS

  • CHRISTOPHER J. EAGLE (a1), ILIJAS FARAH (a2) (a3), BRADD HART (a4), BORIS KADETS (a5), VLADYSLAV KALASHNYK (a6) and MARTINO LUPINI (a7)...

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