Comptes Rendus
Volume articles
Algebra, Functional analysis
Presentations of projective quantum groups
Daniel Gromada1
1 Czech Technical University in Prague, Faculty of Electrical Engineering, Department of Mathematics, Technická 2, 166 27 Praha 6, Czechia
Comptes Rendus. Mathématique, Volume 360 (2022), 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 + .

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.353
Classification: 20G42, 18M25

Daniel Gromada 1

1 Czech Technical University in Prague, Faculty of Electrical Engineering, Department of Mathematics, Technická 2, 166 27 Praha 6, Czechia
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
@article{CRMATH_2022__360_G8_899_0,
     author = {Daniel Gromada},
     title = {Presentations of projective quantum groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {899--907},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
     year = {2022},
     doi = {10.5802/crmath.353},
     language = {en},
}
TY  - JOUR
AU  - Daniel Gromada
TI  - Presentations of projective quantum groups
JO  - Comptes Rendus. Mathématique
PY  - 2022
SP  - 899
EP  - 907
VL  - 360
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.353
LA  - en
ID  - CRMATH_2022__360_G8_899_0
ER  - 
%0 Journal Article
%A Daniel Gromada
%T Presentations of projective quantum groups
%J Comptes Rendus. Mathématique
%D 2022
%P 899-907
%V 360
%I Académie des sciences, Paris
%R 10.5802/crmath.353
%G en
%F CRMATH_2022__360_G8_899_0
Daniel Gromada. Presentations of projective quantum groups. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 899-907. doi : 10.5802/crmath.353. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.353/

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

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

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

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

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

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

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

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

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

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

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

[12] Vijay Kodiyalam; Viakalathur S. Sunder 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

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

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

[15] Moritz Weber 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 | Zbl

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

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

Cited by Sources:

Comments - Policy