scholarly journals Ergodic Actions of Universal Quantum Groups on Operator Algebras

1999 ◽  
Vol 203 (2) ◽  
pp. 481-498 ◽  
Author(s):  
Shuzhou Wang
Keyword(s):  
Quantum Groups ◽  
Operator Algebras ◽  
Universal Quantum

scholarly journals Uprolling unrolled quantum groups

2021 ◽  
pp. 2150023
Author(s):  
Thomas Creutzig ◽  
Matthew Rupert
Keyword(s):  
Quantum Group ◽  
Lie Algebra ◽  
Quantum Groups ◽  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Algebra ◽  
Vertex Operator Algebras ◽  
Roots Of Unity ◽  
Simple Lie Algebra ◽  
Higher Rank

We construct families of commutative (super) algebra objects in the category of weight modules for the unrolled restricted quantum group [Formula: see text] of a simple Lie algebra [Formula: see text] at roots of unity, and study their categories of local modules. We determine their simple modules and derive conditions for these categories being finite, non-degenerate, and ribbon. Motivated by numerous examples in the [Formula: see text] case, we expect some of these categories to compare nicely to categories of modules for vertex operator algebras. We focus in particular on examples expected to correspond to the higher rank triplet vertex algebra [Formula: see text] of Feigin and Tipunin and the [Formula: see text] algebras.

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

Type classification of extreme quantized characters

2019 ◽  
Vol 41 (2) ◽  
pp. 593-605
Author(s):  
RYOSUKE SATO
Keyword(s):  
Dynamical Systems ◽  
Quantum Groups ◽  
Asymptotic Representation ◽  
Operator Algebras ◽  
Complete Solution ◽  
Unitary Groups ◽  
Inductive System ◽  
Von Neumann ◽  
Type Classification

The notion of quantized characters was introduced in our previous paper as a natural quantization of characters in the context of asymptotic representation theory for quantum groups. As in the case of ordinary groups, the representation associated with any extreme quantized character generates a von Neumann factor. From the viewpoint of operator algebras (and measurable dynamical systems), it is natural to ask what is the Murray–von Neumann–Connes type of the resulting factor. In this paper, we give a complete solution to this question when the inductive system is of quantum unitary groups $U_{q}(N)$.

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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