Frobenius胞腔代数 英文PDF电子书下载

1 Frobenius algebras 1

1.1 Definition of Frobenius algebras 1

1.2 Examples of Frobenius algebras 5

1.3 Nakayama automorphisms and Higman ideals 7

1.4 Schur elements of symmetric algebras 13

1.5 Canonical mesh algebras 16

2 Cellular algebras 21

2.1 Definition of cellular algebras 21

2.2 Representation theory of cellular algebras 25

2.3 Quasi-heredity of cellular algebras 28

2.4 A new class of diagram algebras 30

2.5 Standard based algebras 42

2.6 Affine cellular algebras and procellular algebras 48

3 Frobenius cellular algebras 53

3.1 Dual bases 53

3.2 Examples of non-symmetric Frobenius cellular algebras 62

3.3 Symmetric cellular algebras 66

4 Centers and radicals of symmetric cellular algebras 77

4.1 Centers of symmetric cellular algebras 77

4.2 Nakayama twisted centers of Frobenius cellular algebras 88

4.3 Jucys-Murphy elements and centers 91

4.4 Centers of Ariki-Koike algebras 100

4.5 Radicals of symmetric cellular algebras 103

5 Hecke algebras of type A 117

5.1 Murphy basis 117

5.2 Dual Murphy basis 123

5.3 Examples 129

5.4 Kazhdan-Lusztig basis 131

Bibliography 137

Index 144