Related papers: Arithmetic hom-Lie algebras and L-functions
This note being is devoted to the unraveling of the algebraic structure, which governs the quadratic nonhamiltonian interaction of two rotators described in the first part. It should be considered in the context of a general ideology of the…
In this article, Joseph-Louis Lagrange analyzed those numbers which may be represented by the quadratic form $Bt^2 + Ctu + Du^2$. After proving a few theorems on the divisors of such numbers (and their possible forms), Lagrange developed a…
Hom-algebras over a PROP are defined and studied. Several twisting constructions for Hom-algebras over a large class of PROPs are proved, generalizing many such results in the literature. Partial classification of Hom-algebras over a PROP…
In this paper, we introduce the notion of n-Hom-pre-Lie superalgebras. We investigate the representation theory of n-Hom-pre-Lie superalgebras and we give some related results and structures based on Rota-Baxter operators, O-operators and…
In this paper, we introduce a representation theory of Hom-Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop cohomology theory of Hom-Lie conformal superalgebras and discuss some…
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…
The main goal of this work is to introduce the notion of Hom-M-dendriform algebras which are the dendriform version of Hom-Malcev algebras. In fact they are the algebraic structures behind the $\mathcal{O}$-operator of Hom-pre-Malcev…
In 2014, Wolfgang Rump showed that there exists a correspondence between left nilpotent right R-braces and pre-Lie algebras. This correspondence, established using a geometric approach related to flat affine manifolds and affine torsors,…
We show that given a Hom-Lie algebra one can construct the n-ary Hom-Lie bracket by means of an (n-2)-cochain of given Hom-Lie algebra and find the conditions under which this n-ary bracket satisfies the Filippov-Jacobi identity, there by…
Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal…
In this paper, we study representations of Hom-Lie algebroids, give some properties of Hom-Lie algebroids and discuss equivalent statements of Hom-Lie algebroids. Then, we prove that two known definitions of Hom-Lie algebroids can be…
This paper is the third in a series of papers, the aim of which is to construct algebraic geometry over metabelian Lie algebras.
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
The study of affine Deligne-Lusztig varieties originally arose from arithmetic geometry, but many problems on affine Deligne-Lusztig varieties are purely Lie-theoretic in nature. This survey deals with recent progress on several important…
We introduce representations$^{6-th}$ of Lie algebras, and study the counterparts of the P-B-W Theorem and the Hopf algebra structure for the enveloping algebras of Lie algebras in the context of representations$^{6-th}$ of Lie algebras.
Many features of classical Lie theory generalize to the broader context of algebras over Hopf operads. However, this idea remains largely to be developed systematically. Quasi-shuffle algebras provide for example an interesting illustration…
We look at two examples of homotopy Lie algebras (also known as L_{\infty} algebras) in detail from two points of view. We will exhibit the algebraic point of view in which the generalized Jacobi expressions are verified by using degree…
We introduce the notion of left (and right) quasi-Loday algebroids and a "universal space" for them, called a left (right) omni-Loday algebroid, in such a way that Lie algebroids, omni-Lie algebras and omni-Loday algebroids are particular…
We give the definition of left/right Post-Lie algebras and left/right Post-Hopf algebras and establish a link between those objects. We get a Cartier-Quillen-Milnor-Moore theorem for Post-Hopf algebras. We give another description for free…
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones