We describe the structure of the Lie groups endowed with a leftinvariant symplectic form, called symplectic Lie groups, in terms of semi-direct products of Lie groups, symplectic reduction and principal bundles with affine fiber. This description is particularly nice if the group is Hamiltonian, that is, if the left canonical action of the group on itself is Hamiltonian. The principal tool used...

We use the large N critical point formalism to compute d-dimensional exponents at several orders in 1/N an Ising Gross-Neveu universality class where core interaction includes a Lie group generator. Specifying particular symmetry or taking abelian limit of final recovers known results but also provides expressions for any fermion representation.

The symmetry group method is important and widely used in the reduction and construction of explicit solutions of PDEs (partial differential equations). As shown in [1 – 4], the Lie symmetry group method can be used to find explicit solutions of PDEs using symmetry reduction and construction. This method is known as the classical method. By a classical symmetry group of a system of PDEs we mean...