Related papers: On complete reducibility for infinite-dimensional …
The description of irreducible finite dimensional representations of finite dimensional solvable Lie superalgebras over complex numbers given by V.~Kac is refined. In reality these representations are not just induced from a polarization…
The first aim of this paper is to show that any finite-dimensional reductive Lie algebra and its finite-dimensional completely reducible representation can be embedded into some PC Lie algebra. The second aim is to find the structure of a…
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.
In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
In this paper, we give a purely cohomological interpretation of the extension problem for (super) Lie algebras; that is the problem of extending a Lie algebra by another Lie algebra. We then give a similar interpretation of infinitesimal…
We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates…
Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify the irreducible finite-dimensional…
This paper describes finite dimensionall irreducible representations of both twisted and untwisted Cartan map Lie superalgebras.
We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the…
We begin the study of the representation theory of the infinite Temperley-Lieb algebra. We fully classify its finite dimensional representations, then introduce infinite link state representations and classify when they are irreducible or…
The article is devoted to some ``strange'' phenomena of representation theory and their interrelations. Cross-projective representations of pairs of anticommutative algebras, alloys, their universal envelopping Lie algebras and their…
A complete set of inequivalent realizations of three- and four-dimensional real unsolvable Lie algebras in vector fields on a space of an arbitrary (finite) number of variables is obtained.
This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy…
In the article at hand, we sketch how, by utilizing nilpotency to its fullest extent (Engel, Super Engel) while using methods from the theory of universal enveloping algebras, a complete description of the indecomposable representations may…
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 complete the classification of the finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent elements in classical Lie algebras. This extends earlier work where this classification is…
We prove completeness for the main examples of infinite-dimensional Lie groups and some related topological groups.
In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…
A. Dzhumadil'daev classified all irreducible finite dimensional representations of the simple n-Lie algebra. Using a slightly different approach, we obtain in this paper a complete classification of all irreducible, highest weight modules,…