scholarly journals Correction to: Gluing Compact Matrix Quantum Groups

2021 ◽  
Author(s):  
Daniel Gromada
Keyword(s):  
Quantum Groups ◽  
Matrix Quantum

scholarly journals Some remarks on actions of compact matrix quantum groups onC∗-algebras

1992 ◽  
Vol 153 (1) ◽  
pp. 119-127 ◽  
Author(s):  
Yuji Konishi ◽  
Masaru Nagisa ◽  
Yasuo Watatani
Keyword(s):  
Quantum Groups ◽  
Matrix Quantum

ON MATRIX QUANTUM GROUPS OF TYPE An

2000 ◽  
Vol 11 (09) ◽  
pp. 1115-1146 ◽  
Author(s):  
HO Hai PHUNG
Keyword(s):  
Hopf Algebra ◽  
Quantum Group ◽  
Quantum Groups ◽  
Semi Group ◽  
The Matrix ◽  
Hecke Symmetry ◽  
Matrix Quantum

Given a Hecke symmetry R, one can define a matrix bialgebra ER and a matrix Hopf algebra HR, which are called function rings on the matrix quantum semi-group and matrix quantum groups associated to R. We show that for an even Hecke symmetry, the rational representations of the corresponding quantum group are absolutely reducible and that the fusion coefficients of simple representations depend only on the rank of the Hecke symmetry. Further we compute the quantum rank of simple representations. We also show that the quantum semi-group is "Zariski" dense in the quantum group. Finally we give a formula for the integral.

scholarly journals On the representation theory of partition (easy) quantum groups

2016 ◽  
Vol 2016 (720) ◽  
Author(s):  
Amaury Freslon ◽  
Moritz Weber
Keyword(s):  
Representation Theory ◽  
Quantum Groups ◽  
Matrix Quantum

AbstractCompact matrix quantum groups are strongly determined by their intertwiner spaces, due to a result by S. L. Woronowicz. In the case of

scholarly journals The combinatorics of an algebraic class of easy quantum groups

2014 ◽  
Vol 17 (03) ◽  
pp. 1450016 ◽  
Author(s):  
Sven Raum ◽  
Moritz Weber
Keyword(s):  
Symmetric Group ◽  
Quantum Group ◽  
Permutation Group ◽  
Free Product ◽  
Quantum Groups ◽  
Orthogonal Group ◽  
Point Of View ◽  
Algebraic Point ◽  
Matrix Quantum

Easy quantum groups are compact matrix quantum groups, whose intertwiner spaces are given by the combinatorics of categories of partitions. This class contains the symmetric group Sn and the orthogonal group On as well as Wang's quantum permutation group [Formula: see text] and his free orthogonal quantum group [Formula: see text]. In this paper, we study a particular class of categories of partitions to each of which we assign a subgroup of the infinite free product of the cyclic group of order two. This is an important step in the classification of all easy quantum groups and we deduce that there are uncountably many of them. We focus on the combinatorial aspects of this assignment, complementing the quantum algebraic point of view presented in another paper.

scholarly journals Gluing Compact Matrix Quantum Groups

2020 ◽  
Author(s):  
Daniel Gromada
Keyword(s):  
Quantum Groups ◽  
General Procedure ◽  
Free Products ◽  
Cyclic Groups ◽  
Matrix Quantum

AbstractWe study glued tensor and free products of compact matrix quantum groups with cyclic groups – so-called tensor and free complexifications. We characterize them by studying their representation categories and algebraic relations. In addition, we generalize the concepts of global colourization and alternating colourings from easy quantum groups to arbitrary compact matrix quantum groups. Those concepts are closely related to tensor and free complexification procedures. Finally, we also study a more general procedure of gluing and ungluing.

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