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Classification of quasi-affine Generalized Dynkin Diagrams with Rank $> 5$

Zhengtang Tan, Shouchuan Zhang

Abstract

All quasi-affine connected Generalized Dynkin Diagrams with rank $> 5$ are found. All quasi-affine Nichols (Lie braided) algebras with rank $> 5$ are also found.

Classification of quasi-affine Generalized Dynkin Diagrams with Rank $> 5$

Abstract

All quasi-affine connected Generalized Dynkin Diagrams with rank are found. All quasi-affine Nichols (Lie braided) algebras with rank are also found.
Paper Structure (106 sections, 18 theorems, 3 equations)

This paper contains 106 sections, 18 theorems, 3 equations.

Table of Contents

  1. Introduction and Preliminaries
  2. Properties about arithmetic GDDs
  3. Main result
  4. Quasi-affine GDDs over GDD $1$ of Row $11$ in Table C
  5. Quasi-affine GDDs over GDD $2$ of Row $11$ in Table C
  6. Quasi-affine GDDs over GDD $3$ of Row $11$ in Table C
  7. Quasi-affine GDDs over GDD $4$ of Row $11$ in Table C
  8. Quasi-affine GDDs over GDD $1$ of Row $12$ in Table C
  9. Quasi-affine GDDs over GDD $2$ of Row $12$ in Table C
  10. Quasi-affine GDDs over GDD $3$ of Row $12$ in Table C
  11. Quasi-affine GDDs over GDD $4$ of Row $12$ in Table C
  12. Quasi-affine GDDs over GDD $5$ of Row $12$ in Table C
  13. Quasi-affine GDDs over GDD $6$ of Row $12$ in Table C
  14. Quasi-affine GDDs over GDD $7$ of Row $12$ in Table C
  15. Quasi-affine GDDs over GDD $8$ of Row $12$ in Table C
  16. ...and 91 more sections

Key Result

Lemma 2.1

A GDD is a classical GDD if and only if it is one of classical Type 1-7, Here classical types are listed as follows: \begin{picture}(100, 15) \put(-125, -1){ {\rm Type 1}, $2\le n$.} \put(80, 1){\makebox(0, 0)[t]{$\bullet$}} \put(48, -1){\line(1, 0){33}} \put(10,

Theorems & Definitions (20)

  • Lemma 2.1
  • Definition 2.2
  • Definition 2.3
  • Lemma 2.4
  • Lemma 2.5
  • Lemma 2.6
  • Lemma 2.7
  • Lemma 2.8
  • Lemma 2.9
  • Lemma 2.10
  • ...and 10 more