Related papers: Lie higher derivations of arbitrary triangular alg…

Let $G$ be a real connected Lie group with a left invariant metric $d$, $\mathfrak{g}$ its Lie algebra. In this paper we present a set of interesting upper and lower bounds for $|d\exp_{x}(y)|,\ x,y \in \mathfrak{g}$. If $\textrm{ad}_x$ is…

Locally affine Lie algebras are generalizations of affine Kac--Moody algebras with Cartan subalgebras of infinite rank whose root system is locally affine. In this note we study a class of representations of locally affine algebras…

Let C be a commutative ring with unity. In this article, we show that every Jordan derivation over an upper triangular matrix algebra T_n(C) is an inner derivation. Further, we extend the result for Jordan derivation on full matrix algebra…

A variety of three-dimensional left-covariant differential calculi on the quantum group $SU_q(2)$ is considered using an approach based on global $ U(1) $ -covariance. Explicit representations of possible $q $-Lie algebras are constructed…

In his article "Arithmetic Fujita Approximations", Huayi Chen introduces the notion of an approximable graded algebra and asks if any such algebra is a subalgebra of the graded section ring of a big line bundle on an algebraic variety. We…

In this paper, we explore natural connections among trigonometric Lie algebras, (general) affine Lie algebras, and vertex algebras. Among the main results, we obtain a realization of trigonometric Lie algebras as what were called the…

I consider differential of mapping $f$ of continuous division ring as linear mapping the most close to mapping $f$. Different expressions which correspond to known deffinition of derivative are supplementary. I explore the Gateaux…

In this paper, first we introduce the notion of quadratic Rota-Baxter Lie algebras of arbitrary weight, and show that there is a one-to-one correspondence between factorizable Lie bialgebras and quadratic Rota-Baxter Lie algebras of nonzero…

We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal algebras (or corresponding Hamiltonian operators) associated to Poisson algebras and a quasi-derivation found by Xu.…

M.-P. Sch\"utzenberger asked to determine the support of the free Lie algebra ${\mathcal L}_{{\mathbb Z}_{m}}(A)$ on a finite alphabet $A$ over the ring ${\mathbb Z}_{m}$ of integers $\bmod m$ and all the corresponding pairs of twin and…

Exteded Yangian algebras of orthogonal and symplectic types are defined by the Yang-Baxter RLL relation involving the fundamental R-matrix with $so(n)$ or $sp(2m)$ symmetry. We study representations of highest weight characterized by weight…

We construct explicitly groups associated to specific ternary algebras which extend the Lie (super)algebras (called Lie algebras of order three). It turns out that the natural variables which appear in this construction are variables which…

The invariants of solvable triangular Lie algebras with one nilindependent diagonal element are studied exhaustively. Bases of the invariant sets of all such algebras are constructed using an original algebraic algorithm based on Cartan's…

We continue our study of Hilbert space representations of the Reflection Equation Algebra, again focusing on the algebra constructed from the $R$-matrix associated to the $q$-deformation of $GL(N,\mathbb{C})$ for $0<q<1$. We develop a form…

This work is motivated by an article by Wang, Casati, and Prosen [Phys. Rev. E vol. 89, 042918 (2014)] devoted to a study of ergodicity in two-dimensional irrational right-triangular billiards. Numerical results presented there suggest that…

Let ${\mathcal M}$ be a von Neumann algebra with no central summands of type I$_1$. It is shown that every nonlinear $\xi-$Lie derivation ($\xi\neq 1$) on $\mathcal M$ is an additive derivation.

We introduce a new construction of bilinear invariant forms on Lie algebras, based on the method of graded contractions. The general method is described and the $\Bbb Z_2$-, $\Bbb Z_3$-, and $\Bbb Z_2\otimes\Bbb Z_2$-contractions are found.…

We study sympathetic Lie algebras, namely perfect and complete Lie algebras. They arise among other things in the study of adjoint Lie algebra cohomology. This is motivated by a conjecture of Pirashvili, which says that a non-trivial…

In this paper, we focus on the $(\si,\t)$-derivation theory of Lie conformal superalgebras. Firstly, we study the fundamental properties of conformal $(\si,\t)$-derivations. Secondly, we mainly research the interiors of conformal…

We study a certain class of non-maximal rank contractions of the nilpotent Lie algebra $\frak{g}_{m}$ and show that these contractions are completable Lie algebras. As a consequence a family of solvable complete Lie algebras of non-maximal…