Quantum ax + b Group as Quantum Automorphism Group of k[x]

Topological automorphism groups of compact quantum groups

We study the topological structure of the automorphism groups of compact quantum groups showing that, in parallel to a classical result due to Iwasawa, the connected component of identity of the automorphism group and of the "inner" automorphism group coincide. For compact matrix quantum groups, which can be thought of as quantum analogues of compact Lie groups, we prove that the inner automorphism group is a compact Lie group and the outer automorphism group is discrete. Applications of this to the study of group actions on compact quantum groups are highlighted. We end with the construction …

Quantum group of automorphisms of a finite quantum group

A notion of a quantum automorphism group of a finite quantum group, generalising that of a classical automorphism group of a finite group, is proposed and a corresponding existence result proved.

Quantum automorphism group of the lexicographic product of finite regular graphs

We study the quantum automorphism group of the lexicographic product of two finite regular graphs, providing a quantum generalization of Sabidussi's structure theorem on the automorphism group of such a graph.

Cuntz代数的内自同构群的同伦

Homotopy of inner automorphism groups of Cuntz algebras

研究Cuntz代数内自同构群，通过证明其与自同构群有相同同伦群，得出其与射影酉群同伦类型不同的结论。

Mapping class groups and outer automorphism groups of free groups are C*-simple

We prove that the reduced C*-algebras of centerless mapping class groups and outer automorphism groups of free groups are simple, as are the irreducible pure subgroups of mapping class groups and the analogous subgroups of outer automorphism groups of free groups.

Local automorphisms of the unitary group and the general linear group on a Hilbert space

We prove that every 2-local automorphism of the unitary group or the general linear group on a complex infinite-dimensional separable Hilbert space is an automorphism. Thus these types of transformations are completely determined by their local actions on the two-points subsets of the groups in question.