1. Introduction

  2. Hopf algebras and ribbon categories as basic structures

    1. Hopf algebras and ribbon categories very briefly

    2. Algebras, co-algebras, bi-algebras, and related structures

    3. Tensor categories

  3. Axiomatic approach to S-matrix based on the notion of quantum category

    1. Δ andμand the axioms eliminating loops

    2. The physical interpretation of non-trivial braiding and quasi-associativity

    3. Generalizing the notion of bi-algebra structures at the level of configuration space

    4. Ribbon category as a fundamental structure?

    5. Minimal models and TGD

  4. Some examples of bi-algebras and quantum groups

    1. Simplest bi-algebras

    2. Quantum group Uq(sl(2))

    3. General semisimple quantum group

    4. Quantum affine algebras