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Semisolvability of Semisimple Hopf Algebras of Low Dimension
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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
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
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