Manifolds of smooth maps IV : theorem of De Rham
Maximal ideals in the Lie algebra of vector fields
Monodromy representations of braid groups and Yang-Baxter equations
Motivated by the two dimensional conformal field theory with gauge symmetry, we shall study the monodromy of the integrable connections associated with the simple Lie algebras. This gives a series of linear representations of the braid group whose explicit form is described by solutions of the quantum Yang-Baxter equation.
Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2
Let be the class of all multiloop algebras of finite dimensional simple Lie algebras relative to -tuples of commuting finite order automorphisms. It is a classical result that is the class of all derived algebras modulo their centres of affine Kac-Moody Lie algebras. This combined with the Peterson-Kac conjugacy theorem for affine algebras results in a classification of the algebras in . In this paper, we classify the algebras in , and further determine the relationship between and two...