Quantum symmetry groups and related topics
In hindsight one can define the symmetry groups acting on \(X\) (in a manner preserving the relevant features of \(X\)). These form a category, and the symmetry group of \(X\), say \(\mathrm{Sym}_X\) is a universal object of this category. Thus \(\mathrm{Sym}_X\) is a group acting on \(X\) and every action of a group \(G\) on \(X\) can be viewed simply as a homomorphism from \(G\) to \(\mathrm{Sym}_X\). Here the notion of individual, point transformations will be absent and the categorical approach will be useful. The author works with quantum symmetries of finite or compact structures. The theory is based on actions of compact quantum groups on \(C^\ast\)-algebras. The aim is to present old and new research developments, discussing both the general theory and specific examples. At the end, a list of open problems is given. For the entire collection see [Zbl 1381.81011].
scientific article; zbMATH DE number 6847383