相关论文: The radicals of (Braided) Lie algebras
We report on recent work concerning a new type of generalised Kac-Moody algebras based on the spaces of differentiable mappings from compact manifolds or homogeneous spaces onto compact Lie groups.
Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold…
We develop the Lie theory of Lie-admissible algebras whose product is enriched with higher operations modeled on directed graphs with a view to apply it to the deformation theories controlled by this kind of Lie algebras. We produce…
A Lie atom is essentially a pair of Lie algebras and its deformation theory is that of deformations with respect to one algebra together with a trivialization with respect to the other. Such deformations occur commonly in Algebraic…
We construct irreducible modules for twisted toroidal Lie algebras and extended affine Lie algebras. This is done by combining the representation theory of untwisted toroidal algebras with the technique of thin coverings of modules. We…
We generalize I. Frenkel's orbital theory for non twisted affine Lie algebras to the case of twisted affine Lie algebras using a character formula for certain non-connected compact Lie groups.
The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analyzed, and their generalized Casimir invariants calculated. It is shown that rank one solvable…
A frame-independent formulation of Lie brackets on affine spaces or {\em Lie affebras} introduced in [K.\ Grabowska, J.\ Grabowski \& P.\ Urba\'nski, Lie brackets on affine bundles, {\em Ann.\ Global Anal.\ Geom.} {\bf 24} (2003), 101--130]…
This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results are new. The article can be viewed as a…
We summarise the classification of kinematical Lie algebras in arbitrary dimension and indicate which of the kinematical Lie algebras admit an invariant inner product.
A new structure, based on joining copies of a group by means of a \emph{twist}, has recently been considered to describe the brackets of the two exceptional real Lie algebras of type $G_2$ in a highly symmetric way. In this work we show…
We prove some new formulae for the derivatives of the generalized Gegenbauer polynomials associated to the Lie algebra $A_2$.
We show that there is an equivalence of $\infty$-categories between Lie algebroids and certain kinds of curved Lie algebras. For this we develop a method to study the $\infty$-category of curved Lie algebras using the homotopy theory of…
F-Lie algebras are natural generalisations of Lie algebras (F=1) and Lie superalgebras (F=2). We give finite dimensional examples of F-Lie algebras obtained by an inductive process from Lie algebras and Lie superalgebras. Matrix…
We explain that general differential calculus and Lie theory have a common foundation: Lie Calculus is differential calculus, seen from the point of view of Lie theory, by making use of the groupoid concept as link between them. Higher…
This text provides an introduction and complements to some basic constructions and results in 2-representation theory of Kac-Moody algebras.
In this paper explicit decompositions are provided of the Weyl reflections in affine Lie algebras, in terms of fundamental Weyl reflections.
The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base.…
This is an expository paper in which we explain how basic, standard, results about simple Lie algebras can be obtained by geometric arguments, following ideas of Cartan, Richardson and others.
An algebraic algorithm is developed for computation of invariants ('generalized Casimir operators') of general Lie algebras over the real or complex number field. Its main tools are the Cartan's method of moving frames and the knowledge of…