scholarly journals Grothendieck rings of universal quantum groups

2012 ◽  
Vol 349 (1) ◽  
pp. 80-97 ◽  
Author(s):  
Alexandru Chirvasitu
Keyword(s):  
Quantum Groups ◽  
Universal Quantum ◽  
Grothendieck Rings

scholarly journals Higher ℓ2-Betti Numbers of Universal Quantum Groups

2018 ◽  
Vol 61 (2) ◽  
pp. 225-235 ◽  
Author(s):  
Julien Bichon ◽  
David Kyed ◽  
Sven Raum
Keyword(s):  
Quantum Groups ◽  
Betti Numbers ◽  
Universal Quantum

AbstractWe calculate all l2-Betti numbers of the universal discrete Kac quantum groups as well as their half-liberated counterparts

scholarly journals UNIVERSAL QUANTUM GROUPS

1996 ◽  
Vol 07 (02) ◽  
pp. 255-263 ◽  
Author(s):  
ALFONS VAN DAELE ◽  
SHUZHOU WANG
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Universal Quantum ◽  
Group A ◽  
Matrix Quantum

For each invertible m×m matrix Q a compact matrix quantum group Au(Q) is constructed. These quantum groups are shown to be universal in the sense that any compact matrix quantum group is a quantum subgroup of some of them. Their orthogonal version Ao(Q) is also constructed. Finally, we discuss related constructions in the literature.

scholarly journals On the $${\ell }^2$$ ℓ 2 -Betti numbers of universal quantum groups

2017 ◽  
Vol 369 (3-4) ◽  
pp. 957-975 ◽  
Author(s):  
David Kyed ◽  
Sven Raum
Keyword(s):  
Quantum Groups ◽  
Betti Numbers ◽  
Universal Quantum

scholarly journals Quantum Families of Invertible Maps and Related Problems

2016 ◽  
Vol 68 (3) ◽  
pp. 698-720 ◽  
Author(s):  
Adam Skalski ◽  
Piotr Sołtan
Keyword(s):  
Quantum Groups ◽  
Automorphism Groups ◽  
C Algebra ◽  
Universal Quantum ◽  
Algebra Homomorphisms

AbstractThe notion of families of quantum invertible maps (C*–algebra homomorphisms satisfying Podleś condition) is employed to strengthen and reinterpret several results concerning universal quantum groups acting on finite quantum spaces. In particular, Wang's quantum automorphism groups are shown to be universal with respect to quantum families of invertible maps. Further, the construction of the Hopf image of Banica and Bichon is phrased in purely analytic language and employed to define the quantum subgroup generated by a family of quantum subgroups or, more generally, a family of quantum invertible maps.

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