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Pythagorean representations of Thompson’s groups. (English) Zbl 1512.22006

Summary: We introduce the Pythagorean C*-algebras and use the category/functor method to construct unitary representations of Thompson’s groups from representations of them. We calculate several examples.

MSC:

22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
20F65 Geometric group theory
20C15 Ordinary representations and characters
46L05 General theory of \(C^*\)-algebras
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[1] Belk, J., Thompson’s Group F, PhD Thesis, Cornell University · Zbl 1085.20021
[2] Bozejko, M.; Speicher, R., An example of a generalized Brownian motion, Comm. Math. Phys., 137, 519-531 (1991) · Zbl 0722.60033
[3] Bozejko, M.; Speicher, R., An example of a generalized Brownian motion II, (Quantum Probability and Related Topics VII (1992), World Scientific: World Scientific Singapore), 67-77 · Zbl 0797.60066
[4] Bozejko, M.; Speicher, R., Interpolation between bosonic and fermionic relations given by generalized Brownian motions, Math. Z., 222, 135-160 (1996) · Zbl 0843.60071
[5] Brothier, A.; Jones, V. F.R., On the Haagerup and Kazhdan properties of R. Thompson’s groups (2018), preprint · Zbl 1515.20212
[6] Brown, L., Ext of certain free product \(C^⁎\)-algebras, J. Operator Theory, 6, 135-141 (1981) · Zbl 0501.46063
[7] Cannon, J. W.; Floyd, W. J.; Parry, W. R., Introductory notes on Richard Thompson’s groups, Enseign. Math., 42, 215-256 (1996) · Zbl 0880.20027
[8] Connes, A., C*-algèbres et géométrie différentielle, C. R. Acad. Sci. Paris, 290, 599-604 (1980) · Zbl 0433.46057
[9] Connes, A.; Landi, G., Noncommutative manifolds, the instanton algebra and isospectral deformations, Comm. Math. Phys., 221, 1, 141-159 (2001) · Zbl 0997.81045
[10] Cuntz, J., Simple C*-algebras, Comm. Math. Phys., 57, 173-185 (1977) · Zbl 0399.46045
[11] Dudko, A.; Medynets, K., Finite factor representations of Higman-Thompson groups, Groups Geom. Dyn., 8, 2, 375-389 (2014) · Zbl 1328.20012
[12] Golan, G.; Sapir, M., On the stabilizers of finite sets of numbers in the R. Thompson group F, St. Petersburg Math. J., 29, 1, 51-79 (2018) · Zbl 1400.20036
[13] Graham, J. J.; Lehrer, G. I., The representation theory of affine Temperley-Lieb algebras, Enseign. Math., 44, 2, 173-218 (1998) · Zbl 0964.20002
[14] Jones, V. F.R., Some unitary representations of Thompson’s groups F and T, J. Algebraic Combin., 1, 1, 1-44 (2017) · Zbl 1472.57014
[15] Jones, V. F.R., A no-go theorem for the continuum limit of a periodic quantum spin chain, Comm. Math. Phys., 357, 1, 295-317 (2018) · Zbl 1397.82025
[16] McClanahan, K., \(C^⁎\)-algebras generated by elements of a unitary matrix, J. Funct. Anal., 107, 439-457 (1992) · Zbl 0777.46033
[17] Nekrashevych, V., Cuntz-Pimsner algebras of group actions, J. Operator Theory, 52, 223-249 (2004) · Zbl 1447.46045
[18] Rieffel, M. A., C*-algebras associated with irrational rotations, Pacific J. Math., 93, 415 (1981) · Zbl 0499.46039
[19] Vershik, A., Nonfree actions of countable groups and their characters, J. Math. Sci., 174, 1, 1-6 (2011) · Zbl 1279.37004
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