On the structure of quantum automorphism groups

2014/11/07 by Voigt, Christian
#FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1411.1939

Abstract

We compute the K -theory of quantum automorphism groups of finite dimensional C^* -algebras in the sense of Wang. The results show in particular that the C^* -algebras of functions on the quantum permutation groups S_n⁺ are pairwise non-isomorphic for different values of n . Along the way we discuss some general facts regarding torsion in discrete quantum groups. In fact, the duals of quantum automorphism groups are the most basic examples of discrete quantum groups exhibiting genuine quantum torsion phenomena.

Related

• Quantum automorphism groups and SO(3)-deformations
• Crossed Product Equivalence of Quantum Automorphism Groups
• Isomorphisms and automorphisms of quantum groups
• Quantum families of quantum group homomorphisms
• Quantum group of automorphisms of a finite quantum group