Related papers: Reeder's Conjecture for Even Orthogonal Lie algebr…
In the paper we propose a proof of Reeder's Conjecture on the graded multiplicities of small representations in the exterior algebra $\Lambda$g for the simple Lie algebras of type B and C.
We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.
In this short note we confirm an analog of a conjecture of James Wiegold for finite dimensional nilpotent Lie algebras.
The Wiegold conjecture holds for the small Ree groups for $k$-tuples where $k \geq 5$.
We give a uniform proof of a significant part of the Cachazo-Douglas-Seiberg-Witten conjecture by using topology and geometry of infinite Grassmannians.
We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.
In this paper we discuss an analogue of the Kac-Weisfeiler conjecture for a certain class of almost commutative algebras. In particular, we prove the Kac-Weisfeiler type statement for rational Cherednik algebras.
Let $G$ be a finite group and let $\textrm{cd}(G)$ be the set of all complex irreducible character degrees of $G.$ In this paper, we show that if $\textrm{cd}(G)=\textrm{cd}(H),$ where $H$ is a finite simple exceptional group of Lie type,…
The Recognition Theorem for graded Lie algebras is an essential ingredient in the classification of finite-dimensional simple Lie algebras over an algebraically closed field of characteristic p > 3. The main goal of this monograph is to…
In this work we state a version of the double extension for homogeneous quadratic Lie super algebras that includes even and odd cases. We prove that any indecomposable, non-simple and homogeneous quadratic Lie super algebra is obtained by…
Let $R$ be a finite commutative ring with identity. In this paper, we give a necessary condition for the existence of an orthogonal decomposition of the special linear Lie algebra over $R$. Additionally, we study orthogonal decompositions…
We present a local and constructive differential geometric description of finite-dimensional solvable and transitive Lie algebras of vector fields. We show that it implies a Lie's conjecture for such Lie algebras. Also infinite-dimensional…
We prove some isomorphisms between exceptional W-algebras associated with exceptional simple Lie algebras.
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.
We provide new sufficient conditions under which Ryser's conjecture holds.
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…
First, we shall formulate and prove Theorem of Lie-Kolchin type for a cone and derive some algebro-geometric consequences. Next, inspired by a recent result of Dinh and Sibony we pose a conjecture of Tits type for a group of automorphisms…
We have already seen simple representations of modular Lie algebras of $A_l$-type and $C_l$-type. We shall further investigate simple representations of $B_l$ type, which turn out to be very similar in methodology as those types except for…
We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.
The main object of study of this paper is the notion of a LieDer pair, i.e. a Lie algebra with a derivation. We introduce the concept of a representation of a LieDer pair and study the corresponding cohomologies. We show that a LieDer pair…