One of the simplest examples of -algebras is the Bershadsky-Polyakov vertex algebra , associated to and the minimal nilpotent element . We study the simple Bershadsky-Polyakov algebra at positive integer levels and obtain a classification of their irreducible modules. In the case , we show that this vertex algebra has a Kazama-Suzuki-type dual isomorphic to the simple affine vertex superalgebra $L_{k'} (osp(1 \vert 2))$ for $k'=-5/4$. This is joint work with D. Adamovic.
Bershadsky-Polyakov vertex algebras at positive integer levels and duality
The Quantified Constraint Satisfaction Problem (QCSP) is the problem to evaluate a sentence of the form
"for all x1 exists y1 ... forall xn exists yn (R1(...) and ... and Rs(...))",
where R1, ..., Rs are relations from a constraint language Gamma. It is known that the complexity of the QCSP depends only on the algebra of polymorphisms of the constraint language. If all constraints are allowed then the QCSP is PSpace-complete. We will discuss what properties of the algebra place the problem in the class NP, what properties place it in the class co-NP, and how PSpace-hardness can be proved if the algebra has no such properties.
Algebraic approach to the Quantified Constraint Satisfaction Problem