{"product_id":"dimer-models-and-calabi-yau-algebras","title":"Dimer Models and Calabi-Yau Algebras","description":"\u003cp\u003eIn 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.\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cb\u003eAuthor:\u003c\/b\u003e Nathan Broomhead\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003ePublisher:\u003c\/b\u003e American Mathematical Soc.\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003ePublished:\u003c\/b\u003e 2012-01-23\u003c\/li\u003e\n\u003cli\u003e\n\u003cb\u003ePages:\u003c\/b\u003e 101\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"American Mathematical Soc.","offers":[{"title":"Default Title","offer_id":62808626790771,"sku":"9780821853085","price":200.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0987\/0812\/8115\/files\/content_960bfaf4-638b-4cf9-af63-592b20397180.jpg?v=1777964766","url":"https:\/\/readaura.store\/products\/dimer-models-and-calabi-yau-algebras","provider":"Read Aura","version":"1.0","type":"link"}