38 citations · 135 across the 25 of their papers we have counts for
14 papers · 1 filter
A Concrete Model for the Quantum Permutation Group on 4 Points
Nicolas Faroß, Moritz Weber
In 2019, Jung-Weber gave an example of a concrete magic unitary , which defines a -algebraic model of the quantum permutation group . We show with the help of a comp…
Sinkhorn algorithm for quantum permutation groups
Ion Nechita, Simon Schmidt, Moritz Weber
We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogona…
Almost all trees have quantum symmetry
Luca Junk, Simon Schmidt, Moritz Weber
From the work of Erdős and Rényi from 1963 it is known that almost all graphs have no symmetry. In 2017, Lupini, Mančinska and Roberson proved a quantum counterpart: Almost all gra…
New products and -extensions of compact matrix quantum groups
Daniel Gromada, Moritz Weber
There are two very natural products of compact matrix quantum groups: the tensor product and the free product . We define a number of further products interpolatin…
Existence of quantum symmetries for graphs on up to seven vertices: a computer based approach
Christian Eder, Viktor Levandovskyy, Julien Schanz +3
The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined b…
Intertwiner spaces of quantum group subrepresentations
Daniel Gromada, Moritz Weber
We consider compact matrix quantum groups whose -dimensional fundamental representation decomposes into an -dimensional and a one-dimensional subrepresentation. Even if w…
Quantum groups based on spatial partitions
Guillaume Cébron, Moritz Weber
We define new compact matrix quantum groups whose intertwiner spaces are dual to tensor categories of three-dimensional set partitions -- which we call spatial partitions. This ext…
Quantum groups with partial commutation relations
Roland Speicher, Moritz Weber
We define new noncommutative spheres with partial commutation relations for the coordinates. We investigate the quantum groups acting maximally on them, which yields new quantum ve…
Unitary Easy Quantum Groups: the free case and the group case
Pierre Tarrago, Moritz Weber
Easy quantum groups have been studied intensively since the time they were introduced by Banica and Speicher in 2009. They arise as a subclass of (-algebraic) compact matrix q…
The full classification of orthogonal easy quantum groups
Sven Raum, Moritz Weber
In 1987, Woronowicz gave a definition of compact matrix quantum groups generalizing compact Lie groups in the setting of noncommutative geometry. About twenty years later, Banica a…
The combinatorics of an algebraic class of easy quantum groups
Sven Raum, Moritz Weber
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…
Easy quantum groups and quantum subgroups of a semi-direct product quantum group
Sven Raum, Moritz Weber
We consider compact matrix quantum groups whose fundamental corepresentation matrix has entries which are partial isometries with central support. We show that such quantum groups…
On the representation theory of partition (easy) quantum groups
Amaury Freslon, Moritz Weber
Compact matrix quantum groups are strongly determined by their intertwiner spaces, due to a result by S.L. Woronowicz. In the case of easy quantum groups, the intertwiner spaces ar…
A Connection between Easy Quantum Groups, Varieties of Groups and Reflection Groups
Sven Raum, Moritz Weber
We present a link between easy quantum groups, discrete groups and combinatorics. By this, we infer new connections between quantum isometry groups, reflection groups, varieties of…