Compact quantum group structures on type-I C ∗ \mathrm{C}^* C ∗ -algebras

[摘要] We prove a number of results having to do with equipping type-I C∗\mathrm{C}^*C∗-algebras with compact quantum group structures, the two main ones being that such a compact quantum group is necessarily co-amenable, and that if the C∗\mathrm{C}^*C∗-algebra in question is an extension of a non-zero finite direct sum of elementary C∗\mathrm{C}^*C∗-algebras by a commutative unital C∗\mathrm{C}^*C∗-algebra then it must be finite-dimensional.

[学科分类] 神经科学

[关键词] Compact quantum group;quantum space;non-commutative topology;type-I C -algebra