Universally defined representations of Lie conformal superalgebras

Abstract

We distinguish a class of irreducible finite representations of 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 $W_n$, $n\ge 0$, 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 $n\ge 2$ are not universally defined.

Presented at ASCM 2005, to appear in J. Symb. Comp

References in corpus (3)

• Formal distribution algebras and conformal algebras
• Finite conformal modules over the N=2,3,4 superconformal algebras
• Simple associative conformal algebras of linear growth