• Corpus ID: 233289832

Second cohomology groups of the Hopf$^*$-algebras associated to universal unitary quantum groups

@inproceedings{Das2021SecondCG,
  title={Second cohomology groups of the Hopf\$^*\$-algebras associated to universal unitary quantum groups},
  author={Biswarup Das and Uwe Franz and Anna Kula and Adam G. Skalski},
  year={2021}
}
We compute the second (and the first) cohomology groups of ∗-algebras associated to the universal quantum unitary groups of not necesarily Kac type, extending our earlier results for the free unitary group U d . The extended setup forces us to use infinitedimensional representations to construct the cocycles. 

References

SHOWING 1-10 OF 20 REFERENCES
Homological properties of quantum permutation algebras
We show that $A_s(n)$, the coordinate algebra of Wang's quantum permutation group, is Calabi-Yau of dimension $3$ when $n\geq 4$, and compute its Hochschild cohomology with trivial coefficients. We
HOMOLOGICAL INVARIANTS OF DISCRETE QUANTUM GROUPS
These are the notes for a mini-course given at the conference “Topological quantum groups and harmonic analysis”, May 15-19, 2017 at SNU (Seoul National University), Korea. We introduce and discuss
Cohomological dimensions of universal cosovereign Hopf algebras
  • J. Bichon
  • Mathematics
    Publicacions Matemàtiques
  • 2018
We compute the Hochschild and Gerstenhaber-Schack cohomological dimensions of the universal cosovereign Hopf algebras, when the matrix of parameters is a generic asymmetry. Our main tools are
UNIVERSAL QUANTUM GROUPS
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
L\'evy-Khintchine decompositions for generating functionals on universal CQG-algebras
We study the first and second cohomology of the $^*$-algebras of the universal unitary and orthogonal quantum groups $U_F^+$ and $O_F^+$. This provides valuable information for constructing and
Quantum Bohr compactification
We introduce a non commutative analog of the Bohr compactification. Starting from a general quantum group G we define a compact quantum group bG which has a universal property such as the universal
Hochschild homology of Hopf algebras and free Yetter–Drinfeld resolutions of the counit
  • J. Bichon
  • Mathematics
    Compositio Mathematica
  • 2012
Abstract We show that if $A$ and $H$ are Hopf algebras that have equivalent tensor categories of comodules, then one can transport what we call a free Yetter–Drinfeld resolution of the counit of $A$
Le Groupe Quantique Compact Libre U(n)
Abstract:The free analogues of U(n) in Woronowicz' theory [Wo2] are the compact matrix quantum groups introduced by Wang and Van Daele. We classify here their irreducible representations. Their
...
1
2
...