Superconformal algebras are graded Lie superalgebras of growth 1, containing a Virasoro subalgebra. They play an important role in Conformal Field Theory. In 1988 Kac and van de Leur made a conjectural list of simple superconformal algebras, which since has been amended with an exceptional superalgebra CK(6). It has been proposed to use conformal superalgebras to attack this conjecture, and Fattori and Kac established a classification of finite simple conformal superalgebras. It still needs to be proved that one can associate a finite conformal superalgebra to each simple superconformal algebra. In this talk we will show how to use the results of Billig-Futorny to prove that every simple superconformal algebra is polynomial, which implies that one can attach to it an affine conformal superalgebra. We will discuss the difference between finite and affine conformal algebras. We also introduce quasi-Poisson algebras and show how to use them to construct known simple superconformal algebras. Quasi-Poisson algebras may be viewed as a refinement of the notion of Novikov algebras. Quasi-Poisson algebras may be used for computations of automorphisms and twisted forms of superconformal algebras.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
