Lie algebra

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Lie algebra

[′lē ‚al·jə·brə]
(mathematics)
The algebra of vector fields on a manifold with additive operation given by pointwise sum and multiplication by the Lie bracket.
References in periodicals archive ?
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.