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Semisolvability of Semisimple Hopf Algebras of Low Dimension.

By: Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2007Copyright date: ©2007Edition: 1st edDescription: 1 online resource (138 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470404789
Subject(s): Genre/Form: Additional physical formats: Print version:: Semisolvability of Semisimple Hopf Algebras of Low DimensionDDC classification:
  • 512.55
LOC classification:
  • QA613.8 -- .N38 2007eb
Online resources:
Contents:
Intro -- Contents -- Introduction and Main Results -- Conventions and Notation -- Chapter 1. Semisimple Hopf Algebras -- 1.1. Algebra structure -- 1.2. Irreducible characters -- 1.3. Coinvariants of Hopf algebra maps -- 1.4. Yetter- Drinfeld modules -- 1.5. Yetter- Drinfeld modules and the character algebra -- 1.6. One dimensional Yetter- Drinfeld modules -- 1.7. H[sup(coB)] as a left coideal of H -- Chapter 2. The Nichols-Richmond Theorem -- 2.1. Irreducible characters of degree 2 -- 2.2. The Nichols-Richmond theorem -- 2.3. An application to D(H) -- 2.4. Existence of proper Hopf subalgebras -- 2.5. Hopf subalgebras of index 3 -- Chapter 3. Quotient Coalgebras -- 3.1. A multiplicity formula -- 3.2. Stable subcoalgebras -- 3.3. Quotients modulo group- like Hopf subalgebras -- 3.4. On the structure of G(H) -- 3.5. A criterion of normality -- Chapter 4. Braided Hopf Algebras -- 4.1. Radford- Majid biproduct construction -- 4.2. Coalgebra structure of R -- 4.3. Hopf subalgebras -- 4.4. Biproducts over finite groups -- 4.5. Cocommutative braided Hopf algebras -- 4.6. Cocommutative braided Hopf algebras over Z[sub(p)] -- 4.7. Transitive actions of central subgroups -- Chapter 5. Cocycle Deformations of Some Hopf Algebras -- 5.1. Lifting from abelian groups -- 5.2. Examples in dimension pq[sup(2)] -- p = 1 mod q -- 5.3. Examples in dimension pq[sup(2)] -- q = 1 mod p -- 5.4. Normal Hopf subalgebras in cocycle twists -- Chapter 6. Dimension 24 -- 6.1. Possible (co)-algebra structures -- 6.2. Upper and lower semisolvability -- Chapter 7. Dimension 30 -- 7.1. Possible (co)-algebra structures -- 7.2. Classification -- Chapter 8. Dimension 36 -- 8.1. Reduction of the problem -- 8.2. Main result -- Chapter 9. Dimension 40 -- 9.1. Reduction of the problem -- 9.2. Main result -- Chapter 10. Dimension 42 -- 10.1. Possible (co)-algebra structures.
10.2. Classification -- Chapter 11. Dimension 48 -- 11.1. First reduction -- 11.2. Further reductions -- 11.3. Main result up to cocycle twists -- 11.4. Main result -- Chapter 12. Dimension 54 -- 12.1. First reduction -- 12.2. Main result -- Chapter 13. Dimension 56 -- 13.1. First reduction -- 13.2. Main result -- Appendix A. Drinfeld Double of H[sub(8)] -- A.1. Structure of D(H[sub(8)]) -- A.2. Proof of Theorem A.1.1 -- A.3. Proof of Theorem A.1.2 -- Bibliography.
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Intro -- Contents -- Introduction and Main Results -- Conventions and Notation -- Chapter 1. Semisimple Hopf Algebras -- 1.1. Algebra structure -- 1.2. Irreducible characters -- 1.3. Coinvariants of Hopf algebra maps -- 1.4. Yetter- Drinfeld modules -- 1.5. Yetter- Drinfeld modules and the character algebra -- 1.6. One dimensional Yetter- Drinfeld modules -- 1.7. H[sup(coB)] as a left coideal of H -- Chapter 2. The Nichols-Richmond Theorem -- 2.1. Irreducible characters of degree 2 -- 2.2. The Nichols-Richmond theorem -- 2.3. An application to D(H) -- 2.4. Existence of proper Hopf subalgebras -- 2.5. Hopf subalgebras of index 3 -- Chapter 3. Quotient Coalgebras -- 3.1. A multiplicity formula -- 3.2. Stable subcoalgebras -- 3.3. Quotients modulo group- like Hopf subalgebras -- 3.4. On the structure of G(H) -- 3.5. A criterion of normality -- Chapter 4. Braided Hopf Algebras -- 4.1. Radford- Majid biproduct construction -- 4.2. Coalgebra structure of R -- 4.3. Hopf subalgebras -- 4.4. Biproducts over finite groups -- 4.5. Cocommutative braided Hopf algebras -- 4.6. Cocommutative braided Hopf algebras over Z[sub(p)] -- 4.7. Transitive actions of central subgroups -- Chapter 5. Cocycle Deformations of Some Hopf Algebras -- 5.1. Lifting from abelian groups -- 5.2. Examples in dimension pq[sup(2)] -- p = 1 mod q -- 5.3. Examples in dimension pq[sup(2)] -- q = 1 mod p -- 5.4. Normal Hopf subalgebras in cocycle twists -- Chapter 6. Dimension 24 -- 6.1. Possible (co)-algebra structures -- 6.2. Upper and lower semisolvability -- Chapter 7. Dimension 30 -- 7.1. Possible (co)-algebra structures -- 7.2. Classification -- Chapter 8. Dimension 36 -- 8.1. Reduction of the problem -- 8.2. Main result -- Chapter 9. Dimension 40 -- 9.1. Reduction of the problem -- 9.2. Main result -- Chapter 10. Dimension 42 -- 10.1. Possible (co)-algebra structures.

10.2. Classification -- Chapter 11. Dimension 48 -- 11.1. First reduction -- 11.2. Further reductions -- 11.3. Main result up to cocycle twists -- 11.4. Main result -- Chapter 12. Dimension 54 -- 12.1. First reduction -- 12.2. Main result -- Chapter 13. Dimension 56 -- 13.1. First reduction -- 13.2. Main result -- Appendix A. Drinfeld Double of H[sub(8)] -- A.1. Structure of D(H[sub(8)]) -- A.2. Proof of Theorem A.1.1 -- A.3. Proof of Theorem A.1.2 -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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