Resumen de Quantum algebras and quivers

Nicolas Guay

• Given a finite quiver (Q) without loops, we introduce a new class of quantum algebras D(Q) which are deformations of the enveloping algebra of a Lie algebra which is a central extension of sln(Π(Q)) where Π(Q) is the preprojective algebra of (Q). When Q is an affine Dynkin quiver of type A, D or E, we can relate them to Γ-deformed double current algebras. We are able to construct functors between different categories of modules over D(Q). We also give some general results about slˆn(A) , for a quadratic algebra A and about gˆ(C[u,v]) , which we use to introduce deformed double current algebras associated to a simple Lie algebra g .