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Title: Dimer models and Calabi-Yau algebras
Author: Broomhead, Nathan
ISNI:       0000 0003 5838 2585
Awarding Body: University of bath
Current Institution: University of Bath
Date of Award: 2008
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In this thesis we use techniques from algebraic geometry and homological algebra, together with ideas from string theory to construct a class of 3-dimensional Calabi-Yau algebras. The Calabi-Yau property appears throughout geometry and string theory and is increasingly being studied in algebra. Dimer models, first studied in theoretical physics, give a way of writing down a class of non-commutative algebras, as the path algebra of a quiver with relations obtained from a 'superpotential'. Some examples are Calabi-Yau and some are not. We consider two types of 'consistency' condition on dimer models, and show that a 'geometrically consistent' dimer model is 'algebraically consistent'. Finally we prove that the algebras obtained from algebraically consistent dimer models are 3-dimensional Calabi-Yau algebras.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available