Related papers: Notes sur l'indice des alg\`ebres de Lie (II)
This article contains: - Proofs of certain results recently obtained by D. Panyushev. - An addendum to the "inequality of Panyushev". - Calculations of indexes of certain contracted Lie algebras. - Examples of additivity of the index of Lie…
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…
These notes form an introduction to Lie algebras and group theory. Most of the material can be found in many works by various authors given in the list of references. The reader is referred to such works for more detail.
We compute the index of a Lie Borel Lie Algbra of a simple Lie algebra.
We give some properties on the index of seaweed subalgebras of the complex Lie algebra $\mathfrak{gl}(n)$ which allow to obtain formulas for the index of some interesting classes of this family and to give new families of Frobenius Lie…
These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.
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…
Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.
This is a survey on extended affine Lie algebras and related types of Lie algebras, which generalize affine Lie algebras.
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.
These are expanded notes of a two-semester course on Lie groups and Lie algebras given by the author at MIT.
Alternative approaches to Lebesgue integration are considered.
These are extended notes of a lecture about the papers 1207.1883 by Esnault-Levine-Wittenberg and 1308.3024 by Wittenberg. The aim is to define the Esnault-Levine-Wittenberg indices, establish their basic properties amd to pose several…
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…
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.
The quasi-filiform Lie algebras of nonzero rank are described. The classifications of filiform and quasi-filiform naturally graded algebras are corrected.
Some fine gradings on the exceptional Lie algebras $\mathfrak{e}_6$, $\mathfrak{e}_7$ and $\mathfrak{e}_8$ are described. This list tries to be exhaustive.
In this article we continue to study $\aleph_0$-injectivity.
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
The index of a seaweed Lie algebra can be computed from its associated meander graph. We examine this graph in several ways with a goal of determining families of Frobenius (index zero) seaweed algebras. Our analysis gives two new families…