Dimer Models and Calabi Yau Algebras is popular PDF and ePub book, written by Nathan Broomhead in 2012-01-23, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Dimer Models and Calabi Yau Algebras can be Read Online from any device for your convenience.
Dimer Models and Calabi Yau Algebras Book PDF Summary
In this article the author uses 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. He further shows that the algebras constructed are examples of non-commutative crepant resolutions (NCCRs), in the sense of Van den Bergh, of Gorenstein affine toric threefolds. 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. The author considers two types of `consistency' conditions on dimer models, and shows that a `geometrically consistent' dimer model is `algebraically consistent'. He proves that the algebras obtained from algebraically consistent dimer models are 3-dimensional Calabi-Yau algebras. This is the key step which allows him to prove that these algebras are NCCRs of the Gorenstein affine toric threefolds associated to the dimer models.
Detail Book of Dimer Models and Calabi Yau Algebras PDF
- Author : Nathan Broomhead
- Release : 23 January 2012
- Publisher : American Mathematical Soc.
- ISBN : 9780821853085
- Genre : Mathematics
- Total Page : 101 pages
- Language : English
- PDF File Size : 15,5 Mb
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