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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, R.I. :
American Mathematical Society,
2011.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1011. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
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| 049 | |a UAMI | ||
| 100 | 1 | |a Broomhead, Nathan, |d 1982- |1 https://id.oclc.org/worldcat/entity/E39PBJycK3wgtrjyTp9byRHgrq | |
| 245 | 1 | 0 | |a Dimer models and Calabi-Yau algebras / |c Nathan Broomhead. |
| 264 | 1 | |a Providence, R.I. : |b American Mathematical Society, |c 2011. | |
| 300 | |a 1 online resource (vii, 86 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 0065-9266 ; |v number 1011 | |
| 500 | |a "Volume 215, number 1011 (second of 5 numbers)." | ||
| 504 | |a Includes bibliographical references (pages 85-86) and index. | ||
| 505 | 0 | |a Introduction -- Introduction to the dimer model -- Consistency -- Zig-zag flows and perfect matchings -- Toric algebras and algebraic consistency -- Geometric consistency implies algebraic consistency -- Calabi-Yau algebras from algebraically consistent dimers -- Non-commutative crepant resolutions. | |
| 588 | 0 | |a Print version record. | |
| 520 | 3 | |a "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." | |
| 546 | |a English. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Toric varieties. | |
| 650 | 0 | |a Calabi-Yau manifolds. | |
| 650 | 0 | |a Noncommutative algebras. | |
| 650 | 0 | |a Geometry, Algebraic. | |
| 650 | 6 | |a Variétés toriques. | |
| 650 | 6 | |a Variétés de Calabi-Yau. | |
| 650 | 6 | |a Algèbres non commutatives. | |
| 650 | 6 | |a Géométrie algébrique. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x General. |2 bisacsh | |
| 650 | 7 | |a Calabi-Yau manifolds |2 fast | |
| 650 | 7 | |a Geometry, Algebraic |2 fast | |
| 650 | 7 | |a Noncommutative algebras |2 fast | |
| 650 | 7 | |a Toric varieties |2 fast | |
| 650 | 7 | |a Calabi-Yau-Mannigfaltigkeit |2 gnd | |
| 650 | 7 | |a Nichtkommutative Algebra |2 gnd | |
| 650 | 7 | |a Torische Varietät |2 gnd | |
| 758 | |i has work: |a Dimer models and Calabi-Yau algebras (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGBrxwtygW74pm8jGYpVYd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Broomhead, Nathan, 1982- |t Dimer models and Calabi-Yau algebras |z 9780821853085 |w (DLC) 2011037713 |w (OCoLC)756377281 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1011. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=3114383 |z Texto completo |
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