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