8 papers · 1 filter
A note on free quantum groups
Teodor Banica
We study the free complexification operation for compact quantum groups, . We prove that, with suitable definitions, this induces a one-to-one correspondence between free…
On the structure of quantum permutation groups
Teodor Banica, Sergiu Moroianu
The quantum permutation group of the set corresponds to the Hopf algebra . This is an algebra constructed with generators and relations, known to b…
Quantum automorphism groups of homogeneous graphs
Teodor Banica
Associated to a finite graph is its quantum automorphism group . The main problem is to compute the Poincaré series of , meaning the series whose…
Quantum automorphism groups of small metric spaces
Teodor Banica
To any finite metric space we associate the universal Hopf $\c^*$-algebra coacting on . We prove that spaces having at most 7 points fall into one of the following c…
Symmetries of a generic coaction
Teodor Banica
If B is C*-algebra of finite dimension n>3 then the finite dimensional irreducible representations of the compact quantum automorphism group of B, say G, have the same fusion rules…
Fusion rules for representations of compact quantum groups
Teodor Banica
We give a survey of some recent results on the fusion semirings of compact quantum groups (computations of and applications to discrete quantum groups) by using the following simpl…