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.

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This is an upper bound of the dimension of electrical Lie algebra.

Electrical networks, electrical lie algebras and lie groups of finite Dynkin type

When one calculates the symmetries of a given differential equation, one finds the generators in the form of vector fields and then computes the Lie brackets to get the structure constants of the particular Lie algebra one has found.

Second-order systems of ODEs admitting three-dimensional lie algebras and integrability

For a Cartan involution [theta] of G, we write g = l + p for the corresponding Cartan decomposition of the Lie algebra g of G and set K := [G.sup.[theta]] = {g [member of] G : [theta](g) = g}.

Classification of irreducible symmetric spaces which admit standard compact Clifford--Klein forms

A Rota-Baxter operator (of weight zero) on a Lie algebra (g, [*,*]) is a linear operator P : g [right arrow] g such that

Rota-Baxter Operators on 3-Dimensional Lie Algebras and the Classical R-Matrices

The ten independent elements of the SO(5) Lie algebra can be identified with (see (6a)-(6c)) the three components of the generator of total spin [??], the total charge operator Q, and the six real and imaginary components of the [??] operator (which "rotates" the AF phase into the SC phases and vice versa).

Superconducting and Antiferromagnetic Phases of Space-Time

If (g, [,]) is a Lie algebra, then (g, [,,]) is a Lts, where [x, y, z] := [[x, y], z] (see [1, 4, 5]).

Hom-Lie Triple System and Hom-Bol Algebra Structures on Hom-Maltsev and Right Hom-Alternative Algebras

In this case the Lie algebra g of G has an Ad(K)-invariant decomposition g = [??] [direct sum] m, where m [subset] g is a linear subspace of g and [??] is the Lie algebra of K.

Homogeneous Geodesies in Generalized Wallach Spaces

Recently, Lie algebra approach was used to study susceptible-infected-susceptible (SIS) epidemic models [10, 11].

Stochastic Models for the Infectivity Function in an Infinite Population of Susceptible Individuals

The symmetry generators [V.sub.k] in (6a) associated with each solution [s.sub.k] are often called solution symmetries and generate the abelian Lie algebra [A.sub.n], while [W.sub.y] is referred to as the homogeneity symmetry.

First Integrals and Hamiltonians of Some Classes of ODEs of Maximal Symmetry

where [lambda] is the spectral parameter and u is a dependent variable, based on a matrix loop algebra [??] associated with a given matrix Lie algebra g, often being simple.

A New Soliton Hierarchy Associated with so(3, R) and Its Conservation Laws

Let g be a simple Lie algebra over C with Dynkin diagram [delta].

l-restricted Q-systems and quantum affine algebras

In this case (4) admits one-dimensional Lie algebra spanned by the base vector

Comparison of exact solutions for heat transfer in extended surfaces of different geometries