Simple Compact Quantum Groups I

Original · EN

The notion of simple compact quantum group is introduced. As non-trivial (noncommutative and noncocommutative) examples, the following families of compact quantum groups are shown to be simple: (a) The universal quantum groups Bᵤ(Q) for Q ∈ GL(n, C) satisfying Q Q = ± Iₙ, n ≥ 2; (b) The quantum automorphism groups Aaut(B, τ) of finite dimensional C*-algebras B endowed with the canonical trace τ %endowed with a tracial functional tr when (B) ≥ 4, including the quantum permutation groups Aaut(Xₙ) on n points (n ≥ 4); (c) The standard deformations Kq of simple compact Lie groups K and their twists Kqᵘ, as well as Rieffel's deformation Kⱼ.