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.