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Deformation Theory Seminar

Wednesday, November 19, 2008 - 2:00pm

Fred Cohen

U Rochester

Location

University of Pennsylvania

DRL 4N30

Murray's lecture on Merkulov Part III has been postponed

The Lie algebra of derivations of a free Lie algebra arises in an analysis of an analogue of the Torelli group associated to the mapping class group of an orientable surface. In this case, the Lie algebra of derivations informs on the group of automorphisms of a free group which induce the identity map on the level of the first homology group. One emerging structure here arises from a classical construction due to I. Schur known as a 'Schur algebra' one for each natural number n. The natural action of the Schur algebras on the 'quadratic derivations' is shown to generate the Lie algebra of derivations of a free Lie algebra. Basic definitions, structures as well as inter-connections will be described. Some of the results here are based on the thesis of my student Tao Jin who is now pursuing a degree in economics.