Related papers: Index a Lie Borel Lie Algebra

We introduce the method of calculation of index of Lie algebras that are factors of the unitriangular Lie algebra with respect to ideals spanned by subsets of root vectors.

We establish combinatorial formulas for the index of a class of matrix Lie algebras whose matrix forms are encoded by strict partial orderings.

We characterize, in a purely algebraic manner, certain linear forms, called stable, on a Lie algebra. As an application, we determine the index of a Borel subalgebra of a semi-simple Lie algebra. Finally, we give an example of a parabolic…

The index of a Lie algebra is an important invariant which arises in several areas, e.g. in the study of coadjoint orbits for a Lie group, in invariant theory and in representation theory. We study the index for several classes of nilpotent…

The index of a Lie algebra is an important algebraic invariant, but it is notoriously difficult to compute. However, for the suggestively-named seaweed algebras, the computation of the index can be reduced to a combinatorial formula based…

We generalize the results in [2] giving a reduction algorithm allowing to compute the index of seaweed subalgebras of classical simple Lie algebras. We thus are able to obtain the index of some interesting families of seaweed subalgebras…

In this paper we prove several theorems about the behavior of index of Lie algebras derived from associative algebras under tensor products of underlying associative algebras.

We describe, up to isomorphism, all locally simple subalgebras of any diagonal locally simple Lie algebra.

We provide explicit formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a complex simple Lie algebra having fixed class of nilpotence.

We present an extremely elementary construction of the simple Lie algebras over the complex numbers in all of their minuscule representations, using the vertices of various polytopes. The construction itself requires no complicated…

This note presents a general theorem about the cohomology of finite dimensional Lie algebras of arbitrary characteristic. As an application we compute the cohomology of the Borel subalgebra of sl(N).

Let g be a complex simple Lie algebra and b a fixed Borel subalgebra of g. We shall describe the abelian ideals of b in a uniform way, that is, independent of the classification of complex simple Lie algebras.

Let $\Lambda$ be a lattice of rank $n$. A Lie algebra on the lattice $\Lambda$ is a Lie algebra ${\cal L}=\oplus_{\lambda\in\Lambda}\,{\cal L}_{\lambda}$ such that $\dim\,{\cal L}_\lambda=1$ for all $\lambda$. In this article, we classify…

We construct the Lie algebra of an n-Lie algebra and we also define the notion of cohomology of an n-Lie algebra.

In this paper, we give upper bounds for the index of the quotient of the Borel subalgebra of a simple Lie algebra or its nilpotent radical by an ad-nilpotent ideal. For the nilpotent radical quotient, our bound is a generalization of the…

We develop a graphical notation to introduce classical Lie algebras. Although this paper deals with well-known results, our pictorial point of view is slightly different to the traditional one. Our graphical notation is fairly elementary…

The adjoint action of a finite group of Lie type on its Lie algebra is studied. A simple formula is conjectured for the number of split semisimple orbits of a given genus. This conjecture is proved for type A, and partial results are…

We determine all spherical algebraic subalgebras in any simple Lie algebra of real rank 1.

This note provides a formula for the character of the Lie algebra of the fundamental group of a surface, viewed as a module over the symplectic group.

The Lie algbera of a compact semisimple Lie group G is determined by the degrees of the irreducible representations of G. However, two different groups can have the same representation degrees.