Takiff superalgebras and Conformal Field Theory

Understand

A class of non-semisimple extensions of Lie superalgebras is studied.

• They are obtained by adjoining to the superalgebra its adjoint representation as an abelian ideal.
• When the superalgebra is of affine Kac-Moody type, a generalisation of Sugawara's construction is shown to give rise to a copy of the Virasoro algebra and so, presumably, to a conformal field theory.
• Evidence for this is detailed for the extension of the affinisation of the superalgebra gl(1|1): Its highest weight irreducible modules are classified using spectral flow, the irreducible supercharacters are computed and a continuum version of the Verlinde formula is verified to give non-negative integer structure coefficients.