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.