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1	Dots and lines : geometric semigroup theory and finite presentability Awang, Jennifer S. January 2015 (has links) Geometric semigroup theory means different things to different people, but it is agreed that it involves associating a geometric structure to a semigroup and deducing properties of the semigroup based on that structure. One such property is finite presentability. In geometric group theory, the geometric structure of choice is the Cayley graph of the group. It is known that in group theory finite presentability is an invariant under quasi-isometry of Cayley graphs. We choose to associate a metric space to a semigroup based on a Cayley graph of that semigroup. This metric space is constructed by removing directions, multiple edges and loops from the Cayley graph. We call this a skeleton of the semigroup. We show that finite presentability of certain types of direct products, completely (0-)simple, and Clifford semigroups is preserved under isomorphism of skeletons. A major tool employed in this is the Švarc-Milnor Lemma. We present an example that shows that in general, finite presentability is not an invariant property under isomorphism of skeletons of semigroups, and in fact is not an invariant property under quasi-isometry of Cayley graphs for semigroups. We give several skeletons and describe fully the semigroups that can be associated to these. 512
2	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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Dots and lines : geometric semigroup theory and finite presentability

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)