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.
DOI : 10.5802/ambp.382
Mots-clés : Compact quantum groups, Quantum isometry group, Spectral triple
Debashish Goswami 1 ; Arnab Mandal 2
@article{AMBP_2019__26_1_55_0, author = {Debashish Goswami and Arnab Mandal}, title = {Quantum {Isometry} {Group} of {Deformation:} {A} {Counterexample}}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {55--65}, publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal}, volume = {26}, number = {1}, year = {2019}, doi = {10.5802/ambp.382}, zbl = {1360.58006}, language = {en}, url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.382/} }
TY - JOUR AU - Debashish Goswami AU - Arnab Mandal TI - Quantum Isometry Group of Deformation: A Counterexample JO - Annales mathématiques Blaise Pascal PY - 2019 SP - 55 EP - 65 VL - 26 IS - 1 PB - Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal UR - https://ambp.centre-mersenne.org/articles/10.5802/ambp.382/ DO - 10.5802/ambp.382 LA - en ID - AMBP_2019__26_1_55_0 ER -
%0 Journal Article %A Debashish Goswami %A Arnab Mandal %T Quantum Isometry Group of Deformation: A Counterexample %J Annales mathématiques Blaise Pascal %D 2019 %P 55-65 %V 26 %N 1 %I Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal %U https://ambp.centre-mersenne.org/articles/10.5802/ambp.382/ %R 10.5802/ambp.382 %G en %F AMBP_2019__26_1_55_0
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] Quantum automorphism groups of homogeneous graphs, J. Funct. Anal., Volume 224 (2005), pp. 243-280 | DOI | MR | Zbl
[2] Quantum automorphism groups of small metric spaces, Pac. J. Math., Volume 219 (2005) no. 1, pp. 27-51 | DOI | MR | Zbl
[3] Quantum symmetry groups of -algebras equipped with orthogonal filtrations, Proc. Lond. Math. Soc, Volume 106 (2013) no. 5, pp. 980-1004 | DOI | MR | Zbl
[4] Quantum group of orientation preserving Riemannian isometries, J. Funct. Anal., Volume 257 (2009) no. 8, pp. 2530-2572 | DOI | MR | Zbl
[5] Quantum isometry groups: examples and computations, Commun. Math. Phys., Volume 285 (2009) no. 2, pp. 421-444 | DOI | MR | Zbl
[6] Quantum isometry groups of the Podles spheres, J. Funct. Anal., Volume 258 (2009) no. 9, pp. 2937-2960 | DOI | MR | Zbl
[7] Quantum isometry groups, Infosys Science Foundation Series, Springer, 2016 | Zbl
[8] Quantum automorphism groups of finite graphs, Proc. Am. Math. Soc., Volume 131 (2003) no. 3, pp. 665-673 | DOI | MR | Zbl
[9] A guide to Quantum groups, Cambridge University Press, 1994 | Zbl
[10] Noncommutative Geometry, Academic Press Inc., 1994 | Zbl
[11] 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] Quantum groups, Proceedings of the International Congress of Mathematicians (Berkeley, 1986). Vol. 1, American Mathematical Society, 1987 | Zbl
[13] On the deformation of rings and algebras, Ann. Math., Volume 79 (1964) no. 1, pp. 59-103 | DOI | MR | Zbl
[14] Quantum group of isometries in classical and noncommutative geometry, Commun. Math. Phys., Volume 285 (2009) no. 1, pp. 141-160 | DOI | MR | Zbl
[15] 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] 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] Notes on compact quantum groups, Nieuw. Arch. Wisk., Volume 16 (1998) no. 1-2, pp. 73-112 | MR | Zbl
[18] 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] Quantum groups and non-commutative geometry, Université de Montréal, Centre de Recherches Mathématiques, 1988 | Zbl
[20] Quantum symmetry groups of finite spaces, Commun. Math. Phys., Volume 195 (1998) no. 1, pp. 195-211 | DOI | MR | Zbl
[21] Compact matrix pseudogroups, Commun. Math. Phys., Volume 111 (1987), pp. 613-665 | DOI | MR | Zbl
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