On Finite GK-Dimensional Nichols Algebras over Abelian Groups.

Cover
Title page
List of Tables
Chapter 1. Introduction
1.1. Antecedents
1.2. Points and blocks
1.3. The main result
1.3.1. The class of braided vector spaces
1.3.2. Diagonal type
1.3.3. Flourished graphs
1.3.4. Organization of the paper and scheme of the proof
1.3.5. About the proofs
1.3.6. The Poseidon Nichols algebras
1.4. Applications
1.4.1. Examples of Hopf algebras
1.4.2. Domains
1.4.3. Co-Frobenius Hopf algebras
Chapter 2. Preliminaries
2.1. Conventions
2.2. Nichols algebras of diagonal type
2.3. On the Gelfand-Kirillov dimension
2.3.1. Basic facts
2.3.2. A criterium for infinite \GK
Chapter 3. Yetter-Drinfeld modules of dimension 2
3.1. Indecomposable modules and blocks
3.2. The Jordan plane
3.3. The super Jordan plane
3.4. Filtrations of Nichols algebras
3.5. Proof of Theorem 3.1.2
Chapter 4. Yetter-Drinfeld modules of dimension 3
4.1. The setting
4.1.1. A block and a point
4.1.2. A pale block and a point
4.1.3. Indecomposable of dimension 3
4.1.4. Notations
4.1.5. Strong interaction
4.2. Weak interaction
4.2.1. Preparations
4.2.2. Proof of Theorem 4.1.3
4.2.3. Proof of Theorem 4.1.1, weak interaction
4.3. The Nichols algebras with finite \GK
4.3.1. The Nichols algebra \cB(\lstr(1,\ghost))
4.3.2. The Nichols algebra \cB(\lstr(-1,\ghost))
4.3.3. The Nichols algebra \cB(\lstr₋(1,\ghost))
4.3.4. The Nichols algebra \cB(\lstr₋(-1,\ghost))
4.3.5. The Nichols algebra \cB(\lstr( ,1))
4.4. Mild interaction
4.4.1. The Nichols algebra \cB(\cyc₁)
Chapter 5. One block and several points
5.1. The setting
5.2. Proof of Theorem 5.1.1 ( =1)
5.2.1. Weak interaction and the algebra
5.2.2. | |=2
5.2.3. | |>
2
5.3. The Nichols algebras with finite \GK, _{\diag} connected.

5.3.1. The Nichols algebra \cB(\lstr( (1|0)₁
)), ∈\G_{ }', ≥3
5.3.2. The Nichols algebra \cB(\lstr( (1|0)₁
)), ∉\G_{∞}
5.3.3. The Nichols algebra \cB(\lstr( (1|0)₂
))
5.3.4. The Nichols algebra \cB(\lstr( (1|0)₃
))
5.3.5. The Nichols algebra \cB(\lstr( (2|0)₁
))
5.3.6. The Nichols algebra \cB(\lstr( (2|1)
))
5.3.7. The Nichols algebra \cB(\lstr( ₂,2))
5.3.8. The Nichols algebra \cB(\lstr( _{ -1}))
5.4. Proof of Theorem 5.1.2 ( =-1)
5.4.1. Connected components of _{\diag}
5.4.2. The Nichols algebra \cB(\cyc₂)
5.4.3. Several components
5.4.4. The Nichols algebras with finite \GK, several connected components in _{\diag}
Chapter 6. Two blocks
6.1. The setting
6.2. ₁=1
6.3. ₁= ₂=-1
Chapter 7. Several blocks, several points
7.1. Notations
7.2. Several blocks, one point
7.3. The Nichols algebras \pos(\bq,\ghost)
7.4. Several blocks, several points
Chapter 8. Appendix
8.1. Nichols algebras over abelian groups
8.1.1. The context
8.1.2. A pale block and a point
8.1.3. The block has =1
8.1.4. The block has =-1
8.1.5. The block has = ∈\G₃'
8.2. Admissible flourished diagrams
Bibliography
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