University of Colorado
McGregor-Dorsey, Zachary Strider.
Some properties of full heaps.
Degree: PhD, Mathematics, 2013, University of Colorado
A full heap is a labeled infinite partially ordered set with labeling taken from the vertices of an underlying Dynkin diagram, satisfying certain conditions intended to capture the structure of that diagram. The notion of full heaps was introduced by R. Green as an affine extension of the minuscule heaps of J. Stembridge. Both authors applied these constructions to make observations of the Lie algebras associated to the underlying Dynkin diagrams. The main result of this thesis, Theorem 4.7.1, is a complete classification of all full heaps over Dynkin diagrams with a finite number of vertices, using only the general notion of Dynkin diagrams and entirely elementary methods that rely very little on the associated Lie theory. The second main result of the thesis, Theorem 5.1.7, is an extension of the Fundamental Theorem of Finite Distributive Lattices to locally finite posets, using a novel analogue of order ideal posets. We apply this construction in an analysis of full heaps to find our third main result, Theorem 5.5.1, an ADE classification of the full heaps over simply laced affine Dynkin diagrams.
Advisors/Committee Members: Richard M. Green, Nathaniel Thiem, Martin E. Walter, J. M. Douglas, Stephen R. Doty.
Subjects/Keywords: ADE Classification; Combinatorial Algebra; Dynkin Diagram; Full Heap; Lie Algebra; Minuscule Representation
to Zotero / EndNote / Reference
APA (6th Edition):
McGregor-Dorsey, Z. S. (2013). Some properties of full heaps. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/28
Chicago Manual of Style (16th Edition):
McGregor-Dorsey, Zachary Strider. “Some properties of full heaps.” 2013. Doctoral Dissertation, University of Colorado. Accessed October 30, 2020.
MLA Handbook (7th Edition):
McGregor-Dorsey, Zachary Strider. “Some properties of full heaps.” 2013. Web. 30 Oct 2020.
McGregor-Dorsey ZS. Some properties of full heaps. [Internet] [Doctoral dissertation]. University of Colorado; 2013. [cited 2020 Oct 30].
Available from: https://scholar.colorado.edu/math_gradetds/28.
Council of Science Editors:
McGregor-Dorsey ZS. Some properties of full heaps. [Doctoral Dissertation]. University of Colorado; 2013. Available from: https://scholar.colorado.edu/math_gradetds/28