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University of Colorado

1. McGregor-Dorsey, Zachary Strider. Some properties of full heaps.

Degree: PhD, Mathematics, 2013, University of Colorado

URL: https://scholar.colorado.edu/math_gradetds/28

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

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} 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 (16^{th} Edition):

McGregor-Dorsey, Zachary Strider. “Some properties of full heaps.” 2013. Doctoral Dissertation, University of Colorado. Accessed October 30, 2020. https://scholar.colorado.edu/math_gradetds/28.

MLA Handbook (7^{th} Edition):

McGregor-Dorsey, Zachary Strider. “Some properties of full heaps.” 2013. Web. 30 Oct 2020.

Vancouver:

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

Pontifical Catholic University of Rio de Janeiro

2. MARTIN PABLO SANTACATTERINA. [en] CLASSIFICATION OF REAL SEMI-SIMPLE LIE ALGEBRAS BY MEANS OF SATAKE DIAGRAMS.

Degree: 2017, Pontifical Catholic University of Rio de Janeiro

URL: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32456

[pt] Iniciamos o trabalho com uma revisão da classificação de álgebras de Lie semi-simples sobre corposo algebraicamente fechados de caracteristica zero a traves dos Diagramas de Dyinkin. Posteriormente estudamos sigma - sistemas normais e classificamos eles a traves de diagramas de Satake. Finalmente estudamos a estrutura das formas reais de álgebras de Lie semi-simples complexas, explicitando a conexão com os diagramas de Satake e fornecenendo assim uma classificação das mesmas.

[en] We begin the work with a review of the classification of semisimple Lie algebras over an algebraically field of characteristic zero through the Dyinkin Diagrams. Subsequently we study sigma - normal systems and classify them through Satake diagrams. Finally we study the structure of the real forms of complex semi-simple Lie algebras, explaining the connection with the Satake diagrams and thus providing a classification of them.

Subjects/Keywords: [pt] ALGEBRA DE LIE; [en] LIE ALGEBRA; [pt] SUBALGEBRA DE CARTAN; [en] CARTAN SUBALGEBRA; [pt] SISTEMA DE RAIZES; [en] ROOT SYSTEM; [pt] DIAGRAMA DE DYNKIN; [en] DYNKIN DIAGRAM; [pt] DIAGRAMA DE SATAKE; [en] SATAKE DIAGRAM; [pt] GRUPO DE WEYL; [en] WEYL GROUP; [pt] FORMA REAL COMPACTA; [en] COMPACT REAL FORM; [pt] DECOMPOSICAO DE CARTAN; [en] CARTAN DECOMPOSITION; [pt] ABELIANO MAXIMAL; [en] MAXIMAL ABELIAN

Record Details Similar Records

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

SANTACATTERINA, M. P. (2017). [en] CLASSIFICATION OF REAL SEMI-SIMPLE LIE ALGEBRAS BY MEANS OF SATAKE DIAGRAMS. (Thesis). Pontifical Catholic University of Rio de Janeiro. Retrieved from http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32456

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

SANTACATTERINA, MARTIN PABLO. “[en] CLASSIFICATION OF REAL SEMI-SIMPLE LIE ALGEBRAS BY MEANS OF SATAKE DIAGRAMS.” 2017. Thesis, Pontifical Catholic University of Rio de Janeiro. Accessed October 30, 2020. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32456.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

SANTACATTERINA, MARTIN PABLO. “[en] CLASSIFICATION OF REAL SEMI-SIMPLE LIE ALGEBRAS BY MEANS OF SATAKE DIAGRAMS.” 2017. Web. 30 Oct 2020.

Vancouver:

SANTACATTERINA MP. [en] CLASSIFICATION OF REAL SEMI-SIMPLE LIE ALGEBRAS BY MEANS OF SATAKE DIAGRAMS. [Internet] [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2017. [cited 2020 Oct 30]. Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32456.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

SANTACATTERINA MP. [en] CLASSIFICATION OF REAL SEMI-SIMPLE LIE ALGEBRAS BY MEANS OF SATAKE DIAGRAMS. [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2017. Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32456

Not specified: Masters Thesis or Doctoral Dissertation