Equivalent Notions of Normal Quantum Subgroups, Compact Quantum Groups with Properties F and FD, and Other Applications

Abstract

The notion of normal quantum subgroup introduced in algebraic context by Parshall and Wang when applied to compact quantum groups is shown to be equivalent to the notion of normal quantum subgroup introduced by the author. As applications, a quantum analog of the third fundamental isomorphism theorem for groups is obtained, which is used along with the equivalence theorem to obtain results on structure of quantum groups with property F and quantum groups with property FD. Other results on normal quantum subgroups for tensor products, free products and crossed products are also proved.

28 pages. Improved version incorporating referee's suggestions and corrections. To appear in Journal of Algebra

References in corpus (2)

• Cosemisimple Hopf algebras are faithfully flat over Hopf subalgebras
• Free unitary groups are (almost) simple

Cited by in corpus (6)

• Modelling questions for quantum permutations
• Quantum actions on discrete quantum spaces and a generalization of Clifford's theory of representations
• On the problem of classifying simple compact quantum groups
• Fundamental isomorphism theorems for quantum groups
• Property (T), property (F) and residual finiteness for discrete quantum groups
• Quantum symmetry groups of noncommutative tori