基本关系和双林格-霍尔代数 英文版PDF电子书下载

1 Introduction 1

1.1 Background 1

1.2 Main results 2

1.3 Organization 8

2 Preliminaries 10

2.1 Finitary algebras and their Ringel-Hall algebras 10

2.2 Grothendieck groups and twisted Ringel-Hall algebras 12

2.3 Double Ringel-Hall algebras of hereditary algebras 13

2.4 Representations of tame hereditary algebras 18

3 Ringel-Hall algebras and the fundamental relations 22

3.1 Fundamental relations 22

3.2 Higher order fundamental relations 29

3.3 Composition monoid algebra QMc 32

3.4 Quotients of Ringel-Hall algebras 38

4 Subalgebras of Ringel-Hall algebras of tame quivers 45

4.1 Hopf subalgebras of D(A) 45

4.2 Double Ringel-Hall algebras of cyclic quivers 47

4.3 Acyclic quivers of type ？ 55

5 Finite dimensional weight D(△2)-modules 61

5.1 Finite dimensional irreducible representations of Uv(？l2） 61

5.2 Finite dimensional weight D(△2)-modules arising from Uv(？l2)-modules 65

5.3 Finite dimensional weight D(△2)-modules arising from Uv(？l2)-modules 75

References 81