March 26, 2013 -
2:00 pm to 3:00 pm
Location: Cupples I, Room 6 |
Host: Prof. John Shareshian
A Senior Honors Thesis Presentation.
Abstract: Shellability is a property of simplicial complexes that indicates whether the complex can be built up in a "nice" way from its constituent facets. Shellability has been found to have some interesting implications in unexpected places. Specifically, it relates to the order complex associated with the subgroup lattice (which is by definition a partially ordered set), with the partial order relation being set inclusion. The order complex associated with a poset is the simplicial complex created when the elements of the poset are considered vertices, and the totally ordered subsets are considered faces. It has been shown that a finite group is solvable if and only if the order complex associated with its subgroup lattice is shellable. It is therefore of interest to consider the implications of shellability as applied to other types of mathematical structures, such as Lie algebras. As of yet, little is known about the implications of shellability as applied to Lie algebras, and there are few known examples of nonshellable Lie algebras. To that end, in this paper we demonstrate the nonshellability of a small (dimension 6) Lie algebra. To strengthen the correspondence with the result in group theory, the Lie algebra has been chosen to be simple and the underlying field is Z_2.
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