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

Abstract

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 CK 6 , for which E(1, 6) is the annihilation algebra.

Classification of finite irreducible conformal modules over a class of Lie conformal algebras of Block type

“…Finite simple Lie conformal algebras were classified in [9], which shows that a finite simple Lie conformal algebra is isomorphic to either the Virasoro conformal algebra or a current conformal algebra Cur g over a simple finite-dimensional Lie algebra g. The theory of conformal modules and their extensions was developed in [7,8], and the cohomology theory was developed in [2] and further in [11]. For super cases, the structure and representation theories have also been developed in recent years, see [5,14,15,20] and the references therein.…”

Classification of finite irreducible conformal modules over Lie conformal superalgebras of Block type

“…0,α , V ∆,±2∆,α in Proposition 4.10 and Proposition 4.11 (1), is also true for reducible K 2 -modules K…”

“…If max{j G , j J } < k, then Ω(J) = Ω(G) = ∅. One can prove the claim as in Lemma 3.5 (1). If j J = k, then Ω(J) = ∅.…”

“…The most physically important Cartan type Lie conformal superalgebras include the Virasoro conformal algebra K 0 , the Neveu-Schwarz conformal algebra K 1 , and the N = 2 conformal superalgebra K 2 . For the classification of finite irreducible conformal modules (FICMs) over finite simple Lie conformal superalgebras, see [1][2][3][4][5]10].…”

On the Hochschild Cohomologies of Associative Conformal Algebras with a Finite Faithful Representation

“…Structure theory of finite Lie conformal algebras was developed in [15], simple and semisimple finite Lie conformal superalgebras were described in [12,18,19]. Representations and cohomologies of conformal algebras were studied in [2,10,9,11,13,14,29].…”