Quantum algebras associated to quivers and reflection functors

Nicolas Guay (Edinburgh)

Wednesday 21st May, 2008 16:00-17:00 214


I will explain how to contruct new quantum algebras which can be thought of as the Lie analogs of the deformed preprojective algebras for wreath products of W.L. Gan and V. Ginzburg. They are deformations of the enveloping algebra of the universal central extension of $\mathfrak{sl}_n(\Pi(Q))$ where $\Pi(Q)$ is the preprojective algebra of a quiver $Q$. Some important tools in the study of representations of deformed preprojective algebras are the reflection functors which relate categories of representations for different deformation parameters. I will explain how it is possible to construct similar functors for those quantum algebras associated to quivers.

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