Related papers: Classification of uniformly bounded simple Lie con…

Classical affine Lie algebras appear e.g. as symmetries of infinite dimensional integrable systems and are related to certain differential equations. They are central extensions of current algebras associated to finite-dimensional Lie…

Let $\Lambda$ be a lattice of rank $n$. A Lie algebra on the lattice $\Lambda$ is a Lie algebra ${\cal L}=\oplus_{\lambda\in\Lambda}\,{\cal L}_{\lambda}$ such that $\dim\,{\cal L}_\lambda=1$ for all $\lambda$. In this article, we classify…

Let $(\mathcal{G},\nu)$ be a $t$-discrete ergodic groupoid. Consider a finite Von Neumann algebra $\mathcal{M}$ with separable predual. We prove that every uniformly bounded measurable representation $\rho:\mathcal{G} \rightarrow…

The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (a)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…

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.…

A constructive procedure is given to determine all ideals of a solvable Lie algebra. This is used in determining algorithmically all conjugacy classes of subalgebras of a given solvable Lie algebra.

We discuss possible notions of conformal Lie algebras, paying particular attention to graded conformal Lie algebras with $d$-dimensional space isotropy: namely, those with a $\mathfrak{co}(d)$ subalgebra acting in a prescribed way on the…

In this paper we introduce a notion of vertex Lie algebra U, in a way a "half" of vertex algebra structure sufficient to construct the corresponding local Lie algebra L(U) and a vertex algebra V(U). We show that we may consider U as a…

It is shown that any finite dimensional simple Lie superalgebra over an algebraically closed field of characteristic 0 is generated by 2 elements.

Let $L$ be a Lie algebra of Block type over $\C$ with basis $\{L_{\alpha,i}\,|\,\alpha,i\in\Z\}$ and brackets $[L_{\alpha,i},L_{\beta,j}]=(\beta(i+1)-\alpha(j+1))L_{\alpha+\beta,i+j}$. In this paper, we shall construct a formal distribution…

In this paper, a new class of $\Z$-graded Lie conformal algebras $\CW(a,c)$ of infinite rank is constructed. The conformal derivations and one-dimensional central extensions of $\CW(a,c)$ are completely determined. And all conformal modules…

This paper develops techniques for producing presentations of upper cluster algebras. These techniques are suited to computer implementation, and will always succeed when the upper cluster algebra is totally coprime and finitely generated.…

We extend the classification of solvable Lie algebras with abelian nilradicals to classify solvable Leibniz algebras which are one dimensional extensions of an abelian nilradicals.

We consider finitely generated normal algebras over an algebraically closed field of characteristic zero that come with a complexity one grading by a finitely generated abelian group such that the conditions of a UFD are satisfied for…

This paper deals with the classification of Leibniz central extensions of a naturally graded filiform Lie algebra. We choose a basis with respect to that the table of multiplication has a simple form. In low dimensional cases isomorphism…

We obtain an exhaustive classification of totally umbilical surfaces in unimodular and non-unimodular simply-connected 3-dimensional Lie groups endowed with arbitrary left-invariant Riemannian metrics. This completes the classification of…

In this note we provide a direct proof of the complete classification of conformally flat isoparametric submanifolds of Euclidean space.

Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…

We study the problem of the existence of filtered multiplicative bases of a restricted enveloping algebra u(L), where L is a finite-dimensional and p-nilpotent restricted Lie algebra over a field of positive characteristic p.

Regular and higher regular graded algebras (in simplest case satisfying Von Neumann regularity $\Theta_{1}\Theta_{2}\Theta_{1}=\Theta_{1}$ instead of anticommutativity) are introduced and their properties are studied. They are described in…