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Liberation theory for noncommutative homogeneous spaces
Teodor Banica
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 26 (2017) no. 1, p. 127-156

We discuss the liberation question, in the homogeneous space setting. Our first series of results concerns the axiomatization and classification of the families of compact quantum groups G=(G N ) which are “uniform”, in a suitable sense. We study then the quotient spaces of type X=(G M ×G N )/(G L ×G M-L ×G N-L ), and the liberation operation for them, with a number of algebraic and probabilistic results.

On étudie le problème de liberation, dans le cadre des espaces homogènes. Notre première série de résultats concerne l’axiomatisation et la classification des familles de groupes quantiques compacts G=(G N ) qui sont « uniformes », dans un sens convenable. On étudie ensuite les espaces quotient du type X=(G M ×G N )/(G L ×G M-L ×G N-L ), et l’opération de liberation pour ces espaces, avec des résultats de nature algébrique et probabiliste.

Received : 2015-12-14
Accepted : 2016-03-07
Published online : 2017-02-07
DOI : https://doi.org/10.5802/afst.1527
Classification:  46L65,  46L54
Keywords: Liberation theory, Homogeneous space
     author = {Teodor Banica},
     title = {Liberation theory for noncommutative homogeneous spaces},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 26},
     number = {1},
     year = {2017},
     pages = {127-156},
     doi = {10.5802/afst.1527},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_2017_6_26_1_127_0}
Banica, Teodor. Liberation theory for noncommutative homogeneous spaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 26 (2017) no. 1, pp. 127-156. doi : 10.5802/afst.1527. afst.centre-mersenne.org/item/AFST_2017_6_26_1_127_0/

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