Sponsored by Elizabethtown College, Franklin and Marshall College, Lebanon Valley College, and Millersville University
16 September: Ziva Myer, Bryn Mawr College 14 October: Vince Coll, Lehigh University 4 November: Carl Droms, James Madison University 2 December: Evan Folkestad, Franklin and Marshall CollegeTGTS is a regional mathematics seminar/colloquium. We meet at 4:30 p.m. on the first Friday of each month during the academic year (with some exceptions, as noted in the schedule above). The public is cordially invited to attend.
Date: 14 October 2016, 4:30pm Location: Hempfield High School, Room 213 Speaker: Vincent E. Coll Title: Seaweed and poset algebras -- synergies and cohomology Abstract. Part I, Seaweeds. In my previous talk, I introduced seaweed algebras as subalgebras of An = sl(n) and examined certain newly discovered spectral invariants. We have extended the work to the symplectic Type-C case, Cn = sp(2n), and have strong indications of what is true in all other cases – these cases corresponding to the simple Lie algebras in the grand classification. One finds, curiously, that these spectral properties are not unique to Frobenious seaweed subalgebras of the simple Lie algebras. It seems that these properties are shared by certain Lie poset algebras recently introduced by myself and Gerstenhaber in the J. Lie Theory article: Cohomology of Lie semidirect products and poset algebras (2016). Part II, Posets. These Lie poset algebras are concrete matrix algebras and they stand at the nexus of three great cohomology theories: simplicial, the algebraic cohomology of Hochshild, and the Lie algebraic cohomology of Chevalley-Eilenberg. More explicitly, now classic results of Gerstenhaber and Schack elegantly established that simplicial cohomology is a special case of algebraic cohomology. That is, associated to each triangulable space, there is an associative matrix algebra whose algebraic cohomology is the same as the simplicial cohomology of the original space. These matrix algebras are also Lie algebras and therefore have a Lie algebra cohomology which controls their deformations as Lie algebras. We can establish that the latter cohomology is also essentially simplicial and that the deformation theory of these Lie poset algebras is analogous to that of complex analytic manifolds for which this theory is a small model.