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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
(D) a generalization of Iwahori's criterion for finite dimensional representations of real semisimple Lie algebras to admit certain structures (see Proposition 2.9).
Their topics include finite groups: basic structure theory, three-dimensional Lie groups, representations of simple Lie algebras, applications to the construction of ortho-normal bases of states, and space-time symmetries and their representations.
First let us write down the form of the 5 x 5 matrix generators of the Lie algebras of SD(4, 1), iSD(3, 1), and SD(3, 2) in the following suggestive form [7, p.
A connection between solutions of the classical Yang-Baxter equation and quasi-Frobenius Lie algebras was studied by Drinfel'd [23].
It is well-known that Lie algebras are related to associative algebras via the commutator bracket construction.
Let g and [??] be the Lie algebras of G and K respectively and let
Leach, "Symmetry Lie algebras of nth order ordinary differential equations," Journal of Mathematical Analysis and Applications, vol.
It is known that soliton hierarchies such as the Ablowitz-Kaup-Newell-Segur hierarchy and the Kaup-Newell hierarchy are generated from spectral problems associated with matrix Lie algebras [8].
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. J.
The Lie bracket on their Lie algebras is still the matrix commutator.