Related papers: Notes sur l'indice des alg\`ebres de Lie (I)
The Lie algebras over the algebra of dual numbers are introduced and investigated.
Given a simple connected graph on $N$ vertices with size $|E|$ and degree sequence $d_{1}\leq d_{2}\leq ...\leq d_{N}$, the aim of this paper is to exhibit new upper and lower bounds for the additive degree-Kirchhoff index in closed forms,…
We compare the results of our two papers with the results of the paper Aratyn H., Gomes J.F., Zimerman A.H., Higher order Painlev\'e equations and their symmetries via reductions of a class of integrable models, J. Phys. A: Math. Theor., V.…
In this note, we give a slight improvement of a result of A. K\"uronya and V. Lozovanu about higher syzygies on abelian surfaces.
A review is given of some recently obtained results on analytic contractions of Lie algebras and Lie groups and their applications to special function theory.
In this note a characterization of anallytically Riesz operators is given. This work completes the article [1].
The index of a complex Lie algebra is the minimal codimension of its coadjoint orbits. Let us suppose $\g$ semisimple, then its index, ${\rm ind} \g$, is equal to its rank, ${\rm rk \g}$. The goal of this paper is to establish a simple…
We present a method for associating labeled directed graphs to finite-dimensional Lie algebras, thereby enabling rapid identification of key structural algebraic features. To formalize this approach, we introduce the concept of…
The purpose of this note is to provide a detailed proof of Nazarov's inequality stated in Lemma A.1 in Chernozhukov, Chetverikov, and Kato (2017, Annals of Probability).
We introduce a new class of possibly infinite dimensional Lie algebras and study their structural properties. Examples of this new class of Lie algebras are finite dimensional simple Lie algebras containing a nonzero split torus, affine and…
In this short note we confirm an analog of a conjecture of James Wiegold for finite dimensional nilpotent Lie algebras.
This is an overview article on Lie algebroids, and their role as the infinitesimal counterparts of Lie groupoids.
In this paper, we study the index for several natural classes of non-reductive subalgebras of semisimple Lie algebras. Namely, we look at parabolic subalgebras, centralisers of nilpotent elements, and the normalisers of the centralisers. We…
In extending results from Lie to Leibniz algebras, it is helpful to have techniques which translate results from the former to the latter without having to repeat the (perhaps modified) arguments. Such a technique is developed in this work,…
We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.
We investigate coherency properties of certain completed integral group rings, precisely for compact $p$-adic Lie groups.
These notes are devoted to the multiple generalization of a Lie algebra introduced by A.M.Vinogradov and M.M.Vinogradov. We compare definitions of such algebras in the usual and invariant case. Furthermore, we show that there are no simple…
In this paper we investigate the problem of which Lie algebras appear as the derived algebra of a Lie algebra. We present new results that further develop this study and address two questions raised in a paper concerned with the…
The quasi-filiform Lie algebras of nonzero rank are described. The classifications of filiform and quasi-filiform naturally graded algebras are corrected.
A selection of basic results on Borel reducibility of ideals and equivalence relations, especially those with comparably short proofs. This is an unfinished text as yet. Some proofs have missing parts and loose ends. [email protected] and…