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