×

zbMATH — the first resource for mathematics

Pythagorean representations of Thompson’s groups. (English) Zbl 07089431
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:
20 Group theory and generalizations
11 Number theory
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[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)
[5] Brothier, A.; Jones, V. F.R., On the Haagerup and Kazhdan properties of R. Thompson’s groups, (2018), preprint
[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 06684911
[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)
[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
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.