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Deformation Theory Seminar

Wednesday, December 13, 2017 - 2:00pm

Vince Coll

Leheigh U


University of Pennsylvania


A Lie algebra g is Frobenius if there exists a functional f in g* satisfying:  if f([a,b])=0 then a=0.  Such nondegenerate f establish an isomorphism between g and g*.  Let h denote the corresponding element of g.  The spectrum of ad h is an invariant of g, that is, independent of which f is originally chosen.  Here we consider certain algebras – called seaweed algebras – which are subalgebras of the classical Lie algebras.  Remarkably, the spectrum of Frobenius seaweed subalgebras of the classical Lie algebra is an unbroken string of integers.   Here we show that this is true for all the seaweeds in Types A, B, C, and D.  A number of ancillary results pertaining to index formulas for these algebras will also be presented.