Annales Mathématiques
Blaise Pascal
no. 1
Quantum Isometry Group of Deformation: A Counterexample
Debashish Goswami1 ; Arnab Mandal2
1 Indian Statistical Institute 203,B.T.Road Kolkata-700108 INDIA
2 School of Mathematical Sciences National Institute of Science Education and Research Bhuvaneswar, HBNI Jatni-752050 INDIA
Annales mathématiques Blaise Pascal, Tome 26 (2019) no. 1, pp. 55-65.

We give a counterexample to show that the quantum isometry group of a deformed finite dimensional spectral triple may not be isomorphic with a deformation of the quantum isometry group of the undeformed spectral triple.

Publié le :
DOI : 10.5802/ambp.382
Classification : 58B34, 46L87, 46L89
Mots clés : Compact quantum groups, Quantum isometry group, Spectral triple

Debashish Goswami 1 ; Arnab Mandal 2

1 Indian Statistical Institute 203,B.T.Road Kolkata-700108 INDIA
2 School of Mathematical Sciences National Institute of Science Education and Research Bhuvaneswar, HBNI Jatni-752050 INDIA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     pages = {55--65},
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Debashish Goswami; Arnab Mandal. Quantum Isometry Group of Deformation: A Counterexample. Annales mathématiques Blaise Pascal, Tome 26 (2019) no. 1, pp. 55-65. doi : 10.5802/ambp.382. https://ambp.centre-mersenne.org/articles/10.5802/ambp.382/

[1] Teodor Banica Quantum automorphism groups of homogeneous graphs, J. Funct. Anal., Volume 224 (2005), pp. 243-280 | DOI | MR | Zbl

[2] Teodor Banica Quantum automorphism groups of small metric spaces, Pac. J. Math., Volume 219 (2005) no. 1, pp. 27-51 | DOI | MR | Zbl

[3] Teodor Banica; Adam Skalski Quantum symmetry groups of C * -algebras equipped with orthogonal filtrations, Proc. Lond. Math. Soc, Volume 106 (2013) no. 5, pp. 980-1004 | DOI | MR | Zbl

[4] Jyotishman Bhowmick; Debashish Goswami Quantum group of orientation preserving Riemannian isometries, J. Funct. Anal., Volume 257 (2009) no. 8, pp. 2530-2572 | DOI | MR | Zbl

[5] Jyotishman Bhowmick; Debashish Goswami Quantum isometry groups: examples and computations, Commun. Math. Phys., Volume 285 (2009) no. 2, pp. 421-444 | DOI | MR | Zbl

[6] Jyotishman Bhowmick; Debashish Goswami Quantum isometry groups of the Podles spheres, J. Funct. Anal., Volume 258 (2009) no. 9, pp. 2937-2960 | DOI | MR | Zbl

[7] Jyotishman Bhowmick; Debashish Goswami Quantum isometry groups, Infosys Science Foundation Series, Springer, 2016 | Zbl

[8] Julien Bichon Quantum automorphism groups of finite graphs, Proc. Am. Math. Soc., Volume 131 (2003) no. 3, pp. 665-673 | DOI | MR | Zbl

[9] Vyjayanthi Chari; Andrew Pressley A guide to Quantum groups, Cambridge University Press, 1994 | Zbl

[10] Alain Connes Noncommutative Geometry, Academic Press Inc., 1994 | Zbl

[11] Liebrecht De Sadeleer Deformations of spectral triples and their quantum isometry group via monoidal equivalences, Lett. Math. Phys., Volume 107 (2017) no. 4, pp. 673-715 | DOI | MR | Zbl

[12] Vladimir G. Drinfeld Quantum groups, Proceedings of the International Congress of Mathematicians (Berkeley, 1986). Vol. 1, American Mathematical Society, 1987 | Zbl

[13] Murray Gerstenhaber On the deformation of rings and algebras, Ann. Math., Volume 79 (1964) no. 1, pp. 59-103 | DOI | MR | Zbl

[14] Debashish Goswami Quantum group of isometries in classical and noncommutative geometry, Commun. Math. Phys., Volume 285 (2009) no. 1, pp. 141-160 | DOI | MR | Zbl

[15] Debashish Goswami; Soumalya Joardar Quantum isometry group of non commutative manifolds obtained by deformation using dual unitary 2-cocycles, SIGMA, Symmetry Integrability Geom. Methods Appl., Volume 10 (2014), 076, 18 pages | Zbl

[16] Debashish Goswami; Arnab Mandal Quantum isometry group of dual of finitely generated discrete groups and quantum groups, Rev. Math. Phys., Volume 29 (2017), 1750008, 38 pages | DOI | MR | Zbl

[17] Ann Maes; Alfons Van Daele Notes on compact quantum groups, Nieuw. Arch. Wisk., Volume 16 (1998) no. 1-2, pp. 73-112 | MR | Zbl

[18] Arnab Mandal Quantum isometry group of dual of finitely generated discrete groups. II, Ann. Math. Blaise Pascal, Volume 23 (2016) no. 2, pp. 219-247 | DOI | MR | Zbl

[19] Yuri Manin Quantum groups and non-commutative geometry, Université de Montréal, Centre de Recherches Mathématiques, 1988 | Zbl

[20] Shuzhou Wang Quantum symmetry groups of finite spaces, Commun. Math. Phys., Volume 195 (1998) no. 1, pp. 195-211 | DOI | MR | Zbl

[21] Stanisław L. Woronowicz Compact matrix pseudogroups, Commun. Math. Phys., Volume 111 (1987), pp. 613-665 | DOI | MR | Zbl

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