Finite-dimensional Lie groups and

Lie algebras were extensively studied for more than a century, and are well understood.

The 11 papers explore algebraic and combinatorial approaches to the representation theory of

Lie algebras, quantum groups, and algebraic groups.

Reshetikhin, Representations of Yangians and multiplicities of the inclusion of the irreducible components of the tensor product of representations of simple

Lie algebras.

The index theory of

Lie algebras was intensively studied by Elashvili (see [5-8]), in particular the case of semi-simple

Lie algebras and Frobenius

Lie algebras.

Researchers in those and related fields describe recent findings on such matters as Lie group methods for modulus conserving differential equations, the physical realization and implications of the conformal-affine structure of open quantum relativity, the structure and cohomologies of wrap groups of connected fiber bundles, the module structure of the infinite-dimensional

Lie algebra attached to a vector field, deformation and contraction schemes for non-solvable real

Lie algebras up to dimension eight, and the automorphism of some geometric structures on orbifolds.

Urbanski: Tangent and cotangent lifts and graded

Lie algebras associated with Lie algebroids, Ann.

Then Gal(2) and g(2) are

Lie algebras of Gal(2), where

q]) on the

Lie algebras of the unitriangular groups in types B, C and D to define superclasses and supercharacters.

Torsors, reductive group schemes and extended affine

lie algebras.

The subject of Quantum Groups is a rapidly diversifying field of mathematics and mathematical physics, originally launched by developments in theoretical physics and statistical mechanics involving quantum analogues of

Lie algebras and coordinate rings of algebraic groups.

Quantum affine algebras, extended affine

Lie algebras, and their applications; proceedings.

In the end of [LP], Lam and Pylyavskyy suggested a generalization of electrical

Lie algebras to all finite Dynkin types.