no. G8
Algèbre, Analyse fonctionnelle
Presentations of projective quantum groups
Gromada, Daniel1
1 Czech Technical University in Prague, Faculty of Electrical Engineering, Department of Mathematics, Technická 2, 166 27 Praha 6, Czechia
Comptes Rendus. Mathématique, Tome 360 (2022) no. G8, pp. 899-907.

Given an orthogonal compact matrix quantum group defined by intertwiner relations, we characterize by relations its projective version. As a sample application, we prove that PU n + =PO n + .

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.353
Classification : 20G42, 18M25
Gromada, Daniel 1

1 Czech Technical University in Prague, Faculty of Electrical Engineering, Department of Mathematics, Technická 2, 166 27 Praha 6, Czechia 
@article{CRMATH_2022__360_G8_899_0,
     author = {Gromada, Daniel},
     title = {Presentations of projective quantum groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {899--907},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     number = {G8},
     year = {2022},
     doi = {10.5802/crmath.353},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.353/}
}
TY  - JOUR
AU  - Gromada, Daniel
TI  - Presentations of projective quantum groups
JO  - Comptes Rendus. Mathématique
PY  - 2022
SP  - 899
EP  - 907
VL  - 360
IS  - G8
PB  - Académie des sciences, Paris
UR  - http://www.numdam.org/articles/10.5802/crmath.353/
DO  - 10.5802/crmath.353
LA  - en
ID  - CRMATH_2022__360_G8_899_0
ER  - 
%0 Journal Article
%A Gromada, Daniel
%T Presentations of projective quantum groups
%J Comptes Rendus. Mathématique
%D 2022
%P 899-907
%V 360
%N G8
%I Académie des sciences, Paris
%U http://www.numdam.org/articles/10.5802/crmath.353/
%R 10.5802/crmath.353
%G en
%F CRMATH_2022__360_G8_899_0
Gromada, Daniel. Presentations of projective quantum groups. Comptes Rendus. Mathématique, Tome 360 (2022) no. G8, pp. 899-907. doi : 10.5802/crmath.353. http://www.numdam.org/articles/10.5802/crmath.353/

[1] Banica, Teodor Théorie des représentations du groupe quantique compact libre O(n), C. R. Math. Acad. Sci. Paris, Volume 322 (1996), pp. 241-244 | Zbl

[2] Banica, Teodor Le Groupe Quantique Compact Libre U(n), Commun. Math. Phys., Volume 190 (1997) no. 1, pp. 143-172 | DOI | MR | Zbl

[3] Banica, Teodor Symmetries of a generic coaction, Math. Ann., Volume 314 (1999), pp. 763-780 | DOI | MR | Zbl

[4] Banica, Teodor Categorical Formulation of Finite-Dimensional Quantum Algebras, Commun. Math. Phys., Volume 226 (2002), pp. 221-232 | DOI | Zbl

[5] Banica, Teodor; Bichon, Julien; Collins, Benoît The hyperoctahedral quantum group, J. Ramanujan Math. Soc., Volume 22 (2007), pp. 345-384 | MR | Zbl

[6] De Rijdt, An; Vander Vennet, Nikolas Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries, Ann. Inst. Fourier, Volume 60 (2010) no. 1, pp. 169-216 | DOI | Numdam | MR | Zbl

[7] Gromada, Daniel Compact matrix quantum groups and their representation categories, Ph. D. Thesis, Saarland University (2020) | DOI

[8] Gromada, Daniel Quantum symmetries of Cayley graphs of abelian groups (2021) | arXiv

[9] Gromada, Daniel Gluing Compact Matrix Quantum Groups, Algebr. Represent. Theory, Volume 25 (2022), pp. 53-88 | DOI | MR | Zbl

[10] Gromada, Daniel; Weber, Moritz Generating linear categories of partitions (2019–21) (to appear in Kyoto J. Math.) | arXiv

[11] Gromada, Daniel; Weber, Moritz New products and ℤ 2 -extensions of compact matrix quantum groups, Ann. Inst. Fourier, Volume 72 (2022) no. 1, pp. 387-434 | DOI | MR | Zbl

[12] Kodiyalam, Vijay; Sunder, Viakalathur S. Temperley–Lieb and non-crossing partition planar algebras, Noncommutative Rings, Group Rings, Diagram Algebras and Their Applications (Contemporary Mathematics), Volume 456, American Mathematical Society, 2008, pp. 61-72 | MR | Zbl

[13] Wang, Shuzhou Free products of compact quantum groups, Commun. Math. Phys., Volume 167 (1995) no. 3, pp. 671-692 | DOI | MR | Zbl

[14] Wang, Shuzhou Quantum Symmetry Groups of Finite Spaces, Commun. Math. Phys., Volume 195 (1998) no. 1, pp. 195-211 | DOI | MR | Zbl

[15] Weber, Moritz Introduction to compact (matrix) quantum groups and Banica–Speicher (easy) quantum groups, Proc. Indian Acad. Sci., Math. Sci., Volume 127 (2017) no. 5, pp. 881-933 | DOI | MR | Zbl

[16] Woronowicz, Stanisław L. Compact matrix pseudogroups, Commun. Math. Phys., Volume 111 (1987) no. 4, pp. 613-665 | DOI | MR | Zbl

[17] Woronowicz, Stanisław L. Tannaka–Krein duality for compact matrix pseudogroups. Twisted SU(N) groups, Invent. Math., Volume 93 (1988) no. 1, pp. 35-76 | DOI | MR | Zbl

Cité par Sources :