From periodic quiver mutation to cyclically quantized Weyl algebras
David A. Jordan (U Sheffield)
Wednesday 10th November, 2010 16:00-17:00 204
Quivers with periodic mutation have been studied and classified by Fordy and Marsh. The talk will not go into the general theory but will begin by discussing some simple examples of periodic quiver mutation and the recurrence sequences arising from the corresponding mutation of cluster variables. The recurrence sequences can be modelled by an automorphism of a field of rational functions which, for some examples, is a Poisson automorphism for an appropriate Poisson bracket. Aspects of the recurrence lead one to consider certain Poisson subalgebras and these lead, through a notion of quantisation, to some interesting (at least to the speaker) new examples of noncommutative algebras.