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 ?
Rubtsov, Yang-Baxter equation and deformation of associative and Lie algebras.
Meanders: Sturm Global Attractors, Seaweed Lie Algebras and Classical Yang-Baxter Equation
ii) The pair of the Lie algebras (g, h) is isomorphic (up to outer automorphisms) to the direct sum of the following pairs:
In the end of [LP], Lam and Pylyavskyy suggested a generalization of electrical Lie algebras to all finite Dynkin types.
of Newfoundland, Canada) introduce theory of gradings on Lie algebras, with a focus on classifying gradings on simple finite-dimensional Lie algebras over algebraically closed fields.
Among their topics are the probabilistic zeta function, computing covers of Lie algebras, enumerating subgroups of the symmetric group, groups of minimal order that are not n-power closed, the covering number of small alternating groups, geometric algorithms to resolve Bieberbach groups, the non-abelian tensor product of soluble minimax groups, and the short rewriting systems of finite groups.
Simple Lie Algebras Over Fields of Positive Characteristic; Volume I: Structure Theory, 2nd Edition
We use Rinehart's PBW theorem and adapt the technique used in Jacobson's textbook on Lie algebras to give a "better" basis of the universal envelope of a restricted Lie algebra.
By the classical Lie theory, the Lie algebra of a compact Lie group is a direct product of an abelian Lie algebra and some simple Lie algebras.
The book could serve in a one-semester graduate course introducing Lie superalgebras for students who have a basic knowledge of entry-level graduate algebra and have taken a course in finite-dimensional semi-simple Lie algebras.
Macdonald polynomials and characters of KR modules have been studied extensively in connection with various fields such as statistical mechanics and integrable systems, representation theory of Coxeter groups and Lie algebras (and their quantized analogues given by Hecke algebras and quantized universal enveloping algebras), geometry of singularities of Schubert varieties, and combinatorics.
For future development it is interesting to consider the algebraic Bethe ansatz for deformed Gaudin models related to higher rank Lie algebras.