OF VOLUME 2: The Role of Lie Algebras. Relationships between Lie Groups and Lie Algebras. The Three-Dimensional Rotation Groups. The Structure of Semi-Simple Lie Algebras. Semi-Simple Real Lie… Expand

The Basic Framework. The Structure of Groups. Lie Groups. Representation of Groups--Principal Ideas. Representation of Groups--Developments. Group Theory in Quantum Mechanical Calculations.… Expand

The determination of conjugacy classes within the group of all automorphisms of an affine Kac-Moody algebra is discussed in detail, and the limited role of Cartan preserving automorphisms is… Expand

We introduce a new class of 2-cocycles defined explicitly on the generators of certain multiparameter standard quantum groups. These allow us, through the process of twisting the familiar standard… Expand

A method is given for the determination of Clebsch-Gordan coefficients of finite groups. The Clebsch-Gordan coefficients may be arranged into vectors which are eigenvectors of certain projection… Expand

The general theory is given of the origin dependence of the labelling of electron and phonon states in crystals. All types of space group are considered. The space groups T, O, and C are studied as… Expand

Each supermanifold can be considered as equivalent to a certain family of real manifolds. The Haar integral of a Lie supergroup is defined using this equivalence. A useful general formula is derived… Expand