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1	Finite Generation of Ext-Algebras for Monomial Algebras Cone, Randall Edward 09 December 2010 (has links) The use of graphs in algebraic studies is ubiquitous, whether the graphs be finite or infinite, directed or undirected. Green and Zacharia have characterized finite generation of the cohomology rings of monomial algebras, and thereafter G. Davis determined a finite criteria for such generation in the case of cycle algebras. Herein, we describe the construction of a finite directed graph upon which criteria can be established to determine finite generation of the cohomology ring of in-spoked cycle" algebras, a class of algebras that includes cycle algebras. We then show the further usefulness of this constructed graph by studying other monomial algebras, including d-Koszul monomial algebras and a new class of monomial algebras which we term "left/right-symmetric" algebras. / Ph. D. finite generation cohomology monomial algebras
2	Dehn's Problems And Geometric Group Theory LaBrie, Noelle 01 June 2024 (has links) (PDF) In 1911, mathematician Max Dehn posed three decision problems for finitely presented groups that have remained central to the study of combinatorial group theory. His work provided the foundation for geometric group theory, which aims to analyze groups using the topological and geometric properties of the spaces they act on. In this thesis, we study group actions on Cayley graphs and the Farey tree. We prove that a group has a solvable word problem if and only if its associated Cayley graph is constructible. Moreover, we prove that a group is finitely generated if and only if it acts geometrically on a proper path-connected metric space. As an example, we show that SL(2, Z) is finitely generated by proving that it acts geometrically on the Farey tree. Dehn's Problems The Word Problem Geometric Group Theory Geometric Actions Cayley Graphs Finite Generation Geometry and Topology
3	Reduktionssysteme zur Berechnung einer Auflösung der orthogonalen freien Quantengruppen A<sub>o</sub>(n) / Reduction systems for computing a resolution of the free orthogonal quantum groups A<sub>o</sub>(n) Härtel, Johannes 04 July 2008 (has links) No description available. 510 Mathematik Mathematics and Computer Science Reduktionssysteme Gröbnerbasis nicht-kommutative Algebra Quantengruppe orthogonale freie Quantengruppe Auflösungen Umschreibungssysteme Homologiegruppen Kohomologiegruppen Reduction System Gröbner Basis Noncommutative Algebra Free Orthogonal Quantum Group Quantum Group Resolution Term Rewriting System Homology Group Cohomology Group 31.23 EBGS 150: Finite generation finite presentability

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