The author proves that every semisimple Hopf algebra of dimension less than \(60\) over an algebraically closed field \(k\) of characteristic zero is either upper or lower semisolvable up to a cocycle twist.

Table of Contents

• Introduction and main results
• Conventions and notation
• Semisimple Hopf algebras
• The Nichols-Richmond theorem
• Quotient coalgebras
• Braided Hopf algebras
• Cocycle deformations of some Hopf algebras
• Dimension \(24\)
• Dimension \(30\)
• Dimension \(36\)
• Dimension \(40\)
• Dimension \(42\)
• Dimension \(48\)
• Dimension \(54\)
• Dimension \(56\)
• Appendix A. Drinfeld double of \(H_8\)
• Appendix. Bibliography