Lie Conformal Superalgebras Research Articles

Classification of Finite Irreducible Modules over the Lie Conformal Superalgebra CK 6

We classify all continuous degenerate irreducible modules over the exceptional linearly compact Lie superalgebra E(1, 6), and all finite degenerate irreducible modules over the exceptional Lie conformal superalgebra CK6, for which E(1, 6) is the annihilation algebra.

Automorphisms and twisted forms of the $N=1,2,3$ Lie conformal superalgebras

We classify the N = 1, 2, 3 superconformal Lie algebras of Schwimmer and Seiberg by means of differential non-abelian cohomology, and describe the general philosophy behind this new technique. The structure of the group (functor) of automorphisms of the corresponding Lie conformal superalgebra is a key ingredient of the proof.

Universally defined representations of Lie conformal superalgebras

We distinguish a class of irreducible finite representations of the conformal Lie (super)algebras. These representations (called universally defined) are the simplest ones from the computational point of view: a universally defined representation of a conformal Lie (super)algebra L is completely determined by commutation relations of L and by the requirement of associative locality of generators. We describe such representations for conformal superalgebras W n , n ≥ 0 , with respect to a natural set of generators. We also consider the problem for superalgebras K n . In particular, we find a universally defined representation for the Neveu–Schwartz conformal superalgebra K 1 and show that the analogues of this representation for n ≥ 2 are not universally defined.

Representations of simple finite Lie conformal superalgebras of type W and S

We construct all finite irreducible modules over Lie conformal superalgebras of type W and S.

Freely Generated Vertex Algebras and Non?Linear Lie Conformal Algebras

We introduce the notion of a non--linear Lie conformal superalgebra and prove a PBW theorem for its universal enveloping vertex algebra. We also show that conversely any graded freely generated vertex algebra is the universal enveloping algebra of a non--linear Lie conformal superalgebra. This correspondence will be applied in the subsequent work to the problem of classification of finitely generated simple graded vertex algebras.

Classification of finite simple Lie conformal superalgebras

The notion of a Lie conformal superalgebra encodes an axiomatic descrption of singular parts of the operator product expansions of chiral fields in conformal field theory. In the paper we give a detailed proof of the classification of all finite simple Lie conformal superalgebras. We also classify all their central extensions.