1 Frobenius algebras

1.1 Definition of Frobenius algebras

1.2 Examples of Frobenius algebras

1.3 Nakayama automorphisms and Higman ideals

1.4 Schur elements of symmetric algebras

1.5 Canonical mesh algebras

2 Cellular algebras

2.1 Definition of cellular algebras

2.2 Representation theory of cellular algebras

2.3 Quasi-heredity of cellular algebras

2.4 A new class of diagram algebras

2.5 Standard based algebras

2.6 Affine cellular algebras and procellular algebras

3 Frobenius cellular algebras

3.1 Dual bases

3.2 Examples of non-symmetric Frobenius cellular algebras

3.3 Symmetric cellular algebras

4 Centers and radicals of symmetric cellular algebras

4.1 Centers of symmetric cellular algebras

4.2 Nakayama twisted centers of Frobenius cellular algebras

4.3 Jucys-Murphy elements and centers

4.4 Centers of Ariki-Koike algebras

4.5 Radicals of symmetric cellular algebras

5 Hecke algebras of type A

5.1 Murphy basis

5.2 Dual Murphy basis

5.3 Examples

5.4 Kazhdan-Lusztig basis

Bibliography

Index