相关论文: Notes sur l'indice des alg\`ebres de Lie (I)

We give an upper bound for the index of certain Lie algebras, called of seaweed type, introduced by V. Dergachev, A. Kirillov and D. Panyushev. We deduce from this a conjecture of D. Panyushev stated in "Inductive formulas for the index of…

This text is a continuation to "Notes sur l'indice des alg\`ebres de Lie (I)", math.RT/0605499 ----- Ce texte est une suite \`a : "Notes sur l'indice des alg\`ebres de Lie (I)".

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 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…

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…

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.

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. In 2000, Vladimir Dergachev and Alexandre Kirillov defined seaweed subalgebras of $\mathfrak{gl}_n$ (or $\mathfrak{sl}_n$) and provided a formula for the index of a seaweed…

A conjecture of I. Krasikov is proved. Several discrete analogues of classical polynomial inequalities are derived, along with results which allow extensions to a class of transcendental entire functions in the Laguerre-P\'olya class.

For a finite dimensional complex Lie algebra, its index is the minimal dimension of stabilizers for the coadjoint action. A famous conjecture due to Elashvili says that the index of the centralizer of an element of a reductive Lie algebra…

We present a new method of analysis of associative algebras. This method bears a certain resemblance to the famous analysis of commutative $C^*$-algebras in which an important role is played by multiplicative functionals over the algebra.…

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.

This is a short survey on the recent developments made in the integration theory with effective formulas of algebraic structures stronger or higher than Lie algebras.

In this short note, we investigate the following question of Panyushev : ``Is the sum of the index of a parabolic subalgebra of a semisimple Lie algebra $\mathfrak{g}$ and the index of its nilpotent radical always greater than or equal to…

We compute the index of a Lie Borel Lie Algbra of a simple Lie algebra.

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…

A celebrated result of Gromov ensures the existence of a contact structure on any connected, non-compact, odd dimensional Lie group. In general, such structures are not invariant under left translation. The problem of finding which Lie…

We focus on the improvements for Young inequality. We give elementary proof for known results by Dragomir, and we give remarkable notes and some comparisons. Finally, we give new inequalities which are extensions and improvements for the…

Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.

These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.