Related papers: On finite representations of conformal algebras

We prove that a finite torsion-free conformal Lie algebra with a splitting solvable radical has a finite faithful conformal representation.

We prove an analog of the Ado theorem - the existence of a finite-dimensional faithful representation - for a certain kind of finite-dimensional nilpotent Hom-Lie algebras.

Lie conformal algebras appear in the theory of vertex algebras. Their relation is similar to that of Lie algebras and their universal enveloping algebras. Associative conformal algebras play a role in conformal representation theory. We…

We give a natural proof of the Ado theorem.

We describe all irreducible conformal subalgebras of Cend_N. The classification of simple and semisimple associative conformal algebras with finite faithful representation follows from this description.

In this note we present a more detailed and explicit exposition of the definition of a conformal representation of a Leibniz algebra. Recall (arXiv:math/0611501v3) that Leibniz algebras are exactly Lie dialgebras. The idea is based on the…

Associative conformal algebras of conformal endomorphisms are of essential importance for the study of finite representations of conformal Lie algebras (Lie vertex algebras). We describe all semisimple algebras of conformal endomorphisms…

We prove a refinement of Ado's theorem for Lie algebras over an algebraically-closed field of characteristic zero. We first define what it means for a Lie algebra $L$ to be approximated with a nilpotent ideal, and we then use such an…

We give a simple proof of the Birkhoff theorem about existence of a faithful representation for any finite-dimensional nilpotent Lie algebra of characteristic zero.

In this paper, we construct a faithful representation with the lowest dimension for every complex Lie algebra in dimension $\leq 4$. In particular, in our construction, in the case that the faithful representation has the same dimension of…

We show that $\tau$-tilting finite simply connected algebras are representation-finite. Then, some related algebras are considered, including iterated tilted algebras, tubular algebras and so on. We also prove that the $\tau$-tilting…

We study the notion of linear sofic approximations for algebras, analogous to the concept of sofic representations for groups. We prove that for a finitely generated amenable $K$-algebra with no zero divisors, all linear sofic…

A class of representations of a Lie superalgebra (over a commutative superring) in its symmetric algebra is studied. As an application we get a direct and natural proof of a strong form of the Poincare'-Birkhoff-Witt theorem, extending this…

In this paper, we introduce a $\{\lambda_{1\to n-1}\}$-bracket and a distribution notion of an $n$-Lie conformal algebra. For any $n$-Lie conformal algebra $R$, there exists a series of associated infinite-dimensional linearly compact…

Conformal algebras, recently introduced by Kac, encode an axiomatic description of the singular part of the operator product expansion in conformal field theory. The objective of this paper is to develop the theory of ``multi-dimensional''…

We prove that, if A is a strongly simply connected algebra of polynomial growth, then A is torsionless-finite. In particular, its representation dimension is at most three.

We prove that a Lie conformal algebra L with bounded locality function is embeddable into an associative conformal algebra A with the same bound on the locality function. If L is nilpotent, then so is A, and the nilpotency index remains the…

In this paper it is stressed that there is no {\em physical} reason for symmetries to be linear and that Lie group theory is therefore too restrictive. We illustrate this with some simple examples. Then we give a readable review on the…

By Liouville's theorem, in dimensions 3 or more conformal transformations form a finite-dimensional group, an apparent drastic departure from the 2-dimensional case. We propose a derived enhancement of the conformal Lie algebra which is an…

We study quadratic Lie conformal superalgebras associated with No\-vikov superalgebras. For every Novikov superalgebra $(V,\circ)$, we construct an enveloping differential Poisson superalgebra $U(V)$ with a derivation $d$ such that $u\circ…