Yahiatene, Sophiane: Hurwitz action in Coxeter groups and extended Weyl groups with application in representation theory of finite dimensional algebras. 2020
Inhalt
- List of Figures
- Introduction
- Reflection groups and Hurwitz action
- Hurwitz action in Coxeter groups
- Definitions and basic properties
- The canonical simple system of a reflection subgroup
- Hurwitz action on arbitrary reflection factorizations of Coxeter elements
- Hurwitz action in finite Coxeter groups
- Hurwitz action on the set of non-reduced reflection factorizations
- Investigation of quasi-Coxeter elements in finite Coxeter groups
- Hurwitz action in extended Weyl groups
- Definitions and basic properties
- The extended Weyl group
- The conjugacy class and reflection length of Coxeter transformations
- Hurwitz action for the wild and domestic cases
- Hurwitz action for the tubular cases
- Exceptional sequences in abelian categories and thick subcategories
- Abelian categories
- Triangulated categories and the derived category of an abelian category
- The derived category of an abelian category and tilting theory for abelian categories
- Exceptional sequences in abelian and triangulated categories
- Root data attached to triangulated k-categories of finite type
- The category of finitely generated modules over a finite dimensional k-algebra
- Category of coherent sheaves over a weighted projective line
- Thick subcategories generated by an exceptional sequence and the interval poset
- Exceptional sequences and prefixes of reduced generating reflection factorizations of Coxeter transformations
- Thick subcategories generated by an exceptional sequence
- Auxiliary calculations
- References