Related papers: On the structure of quantum automorphism groups

We compute the group homology, the topological K-theory of the reduced C^*-algebra, the algebraic K-theory and the algebraic L-theory of the group ring of the semi-direct product of the three-dimensional discrete Heisenberg group by Z/4.…

Double coverings of the orthogonal groups of the real and complex spaces are considered. The relation between discrete transformations of these spaces and fundamental automorphisms of Clifford algebras is established, where an isomorphism…

We compute the K-theory of the C*-algebra of symmetric words in two universal unitaries. This algebra is the fixed point C*-algebra for the order-two automorphism of the full C*-algebra of the free group on two generators which switches the…

We introduce a new class of C^*-algebras, which is a generalization of both graph algebras and homeomorphism C^*-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the…

We study quantum automorphism group of vertex-transitive graphs using intertwinner spaces of the magic unitary matrix associated to this quantum subgroups of $S_n^+$. We also give some applications to quantum symmetries of circulant graphs…

Let $\Uq$ be a quantum group. Regarding a (noncommutative) space with $\Uq$-symmetry as a $\Uq$-module algebra $A$, we may think of equivariant vector bundles on $A$ as projective $A$-modules with compatible $\Uq$-action. We construct an…

Let $U(KG)$ be the group of units of the group ring $KG$ of the group $G$ over a commutative ring $K$. The anti-automorphism $g\mapsto g\m1$ of $G$ can be extended linearly to an anti-automorphism $a\mapsto a^*$ of $KG$. Let $S_*(KG)=\{x\in…

Many important quantum algebras such as quantum symplectic space, quantum Euclidean space, quantum matrices, $q$-analogs of the Heisenberg algebra and the quantum Weyl algebra are semi-commutative. In addition, enveloping algebras $U(L_+)$…

We investigate the $K$-theory of unital UCT Kirchberg algebras $\mathcal{Q}_S$ arising from families $S$ of relatively prime numbers. It is shown that $K_*(\mathcal{Q}_S)$ is the direct sum of a free abelian group and a torsion group, each…

We study the automorphism group of a unital, simple, $\mathcal{Z}$-stable $C^{*}$-algebra. In this paper, we generalize the results by the authors in \cite{pr_auto} to $\mathcal{Z}$-stable $C^{*}$-algebras $\mathfrak{A}$ such that…

We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…

We reveal a correspondence between the homological torsion of the Bianchi groups and new geometric invariants, which are effectively computable thanks to their action on hyperbolic space. We use it to explicitly compute their integral group…

Topological T-duality correspondences are higher categorical objects that can be classified by a strict Lie 2-group. In this article we compute the categorical automorphism group of this 2-group; hence, the higher-categorical symmetries of…

We determine the $K$-theory of the $C^{*}$-algebra $C(SU_{-1}(2))$ and describe its spectrum. Moreover, we exhibit a continuous $C^{*}$-bundle over $[-1,0)$ whose fibre at $q$ is isomorphic to $C(SU_{q}(2))$.

We investigate the automorphism group of the quantised enveloping algebra U of the positive nilpotent part of certain simple complex Lie algebras g in the case where the deformation parameter q \in \mathbb{C}^* is not a root of unity.…

Let $H$ be the Hopf $C^*$-algebra of continuous functions on a (locally) compact quantum group of either reduced or full type. We show that endomorphisms of $H$ that respect its right regular comodule structure are translations by elements…

The quantum permutation group of the set $X_n=\{1,..., n\}$ corresponds to the Hopf algebra $A_{aut}(X_n)$. This is an algebra constructed with generators and relations, known to be isomorphic to $\cc (S_n)$ for $n\leq 3$, and to be…

The multipullback quantization of complex projective spaces lacks the naive quantum CW-complex structure because the quantization of an embedding of the $n$-skeleton into the $(n+1)$-skeleton does not exist. To overcome this difficulty, we…

We consider the construction of twisted tensor products in the category of C*-algebras equipped with orthogonal filtrations and under certain assumptions on the form of the twist compute the corresponding quantum symmetry group, which turns…

We give a survey of techniques from quantum group theory which can be used to show that some quantum spaces (objects of the category dual to the category of $\mathrm{C}^*$-algebras) do not admit any quantum group structure. We also provide…