Categorification in geometry, topology, and physics /

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The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorification is a powerful tool for relating va...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Beliakova, Anna, 1968- (Editor ), Lauda, Aaron, 1981- (Editor )
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, Rhode Island : American Mathematical Society, [2017]
Colección:Contemporary mathematics (American Mathematical Society) ; v. 684.
Temas:
Categories (Mathematics)
Mathematical analysis.
Topology.
Geometry.
Physics.
Catégories (Mathématiques)
Analyse mathématique.
Topologie.
Géométrie.
Physique.
geometry.
physics.
MATHEMATICS > Algebra > Intermediate.
Geometry
Mathematical analysis
Physics
Topology
Quantum theory > Groups and algebras in quantum theory > Quantum groups and related algebraic methods.
Manifolds and cell complexes > Low-dimensional topology > Knots and links in $S^3$.
Algebraic geometry > (Colo.)homology theory > Sheaves, derived categories of sheaves and related constructions.
Category theory; homological algebra > Categories with structure > Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories.
Global analysis, analysis on manifolds > Partial differential equations on manifolds; differential operators > Eta-invariants, Chern-Simons invariants.
Nonassociative rings and algebras > Lie algebras and Lie superalgebras > Applications to physics.
Group theory and generalizations > Representation theory of groups > Hecke algebras and their representations.
Nonassociative rings and algebras > Lie algebras and Lie superalgebras > Homological methods in Lie (super)algebras.
Nonassociative rings and algebras > Lie algebras and Lie superalgebras > Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Geometry and categorification / Ben Webster
  • A geometric realization of modified quantum algebras / Yiqiang Li
  • The cube and the Burnside category / Tyler Lawson, Robert Lipshitz, Sucharit Sarkar
  • Junctins of surface operators and categorification of quantum groups / Sungbong Chun, Sergei Gukov, Daniel Roggenkamp
  • Khovanov-Rozansky homology and 2-braid groups / Raphaël Rouquier
  • DAHA approach to iterated torus links / Ivan Cherednik, Ivan Danilenko.

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