Dimer models and Calabi-Yau algebras /

"In this article 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 algebr...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Broomhead, Nathan, 1982-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, R.I. : American Mathematical Society, 2011.
Colección:Memoirs of the American Mathematical Society ; no. 1011.
Temas:
Toric varieties.
Calabi-Yau manifolds.
Noncommutative algebras.
Geometry, Algebraic.
Variétés toriques.
Variétés de Calabi-Yau.
Algèbres non commutatives.
Géométrie algébrique.
MATHEMATICS > Geometry > General.
Calabi-Yau manifolds
Geometry, Algebraic
Noncommutative algebras
Toric varieties
Calabi-Yau-Mannigfaltigkeit
Nichtkommutative Algebra
Torische Varietät
Acceso en línea:Texto completo
Descripción
Sumario:"In this article 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. We further show 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. We consider two types of 'consistency' conditions on dimer models, and show that a 'geometrically consistent' dimer model is 'algebraically consistent'. We prove that the algebras obtained from algebraically consistent dimer models are 3-dimensional Calabi-Yau algebras. This is the key step which allows us to prove that these algebras are NCCRs of the Gorenstein affine toric threefolds associated to the dimer models."
Notas:"Volume 215, number 1011 (second of 5 numbers)."
Descripción Física:1 online resource (vii, 86 pages) : illustrations
Bibliografía:Includes bibliographical references (pages 85-86) and index.
ISBN:9780821885147
0821885146
ISSN:0065-9266 ;

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