Dimer Models and Calabi-Yau Algebras (eBook)

Nathan Broomhead (Autor)

eBook Download: PDF

86 Seiten
American Mathematical Society (Verlag)
978-0-8218-8514-7 (ISBN)

Infos

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.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 0-8218-8514-6 / 0821885146
• ISBN-13: 978-0-8218-8514-7 / 9780821885147