Four‐dimensional topological quantum field theory, Hopf categories, and the canonical bases

Keywords

Hopf algebra, Quantum field theory, Algebraic structure, Quantum, Field (mathematics)

References

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• P.L. Homeomorphic Manifolds are Equivalent by Elementary 5hellingstUdo Pachner — 1991
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• On crystal bases of the Q-analogue of universal enveloping algebrasMasaki Kashiwara — 1991
• TOPOLOGICAL QUANTUM FIELD THEORIES ASSOCIATED TO FINITE GROUPS AND CROSSED G-SETSDavid N. Yetter — 1992
• 2-d physics and 3-d topologyLouis Crane — 1991
• An instanton-invariant for 3-manifoldsAndreas Floer — 1988
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• State sum invariants of 3 manifolds and quantum 6j symbolsVladimir G. Turaev, Oleg Viro — 1992
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• Braided monoidal 2-categories and Manin-Schechtman higher braid groupsMikhail Kapranov, Vladimir Voevodsky — 1994
• Quantum SU(2)-invariants dominate Casson's SU(2)-invariantHitoshi Murakami — 1994
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• Categories for the Working MathematicianSaunders Mac Lane — 1971
• Canonical bases arising from quantized enveloping algebrasG. Lusztig — 1990
• Involutory Hopf algebras and 3-manifold invariantsGreg Kuperberg — 1990
• Chern-Simons theory with finite gauge groupDaniel S. Freed, Frank Quinn — 1991

Cited by

• Categorification and Group ExtensionsLucian M. Ionescu — 2002
• Foundations of categorified representation theoryAlexander E. Hoffnung — 2010
• On a Trialgebraic Deformation of the Manin PlaneHarald Grosse, Karl-Georg Schlesinger — 2000
• Examples of categorificationLouis Crane, David N. Yetter — 1996
• A duality Hopf algebra for holomorphic N=1 special geometriesKarl-Georg Schlesinger — 2004
• The projective class ring of half-quantum groups at roots of unityClaude Cibils — 1998
• Quantum Leap: From Dirac and Feynman, Across the Universe, to Human Body and MindVladimir G. Ivancevic, Tijana T. Ivancevic — 2008
• Functorial Knot Theory : Categories of Tangles, Coherence, Categorical Deformations and Topological InvariantsDavid N. Yetter — 2001
• Spin networks and the bracket polynomialLouis H. Kauffman — 1998
• Representation theory of 2-groups on Kapranov and Voevodsky's 2-vector spacesJosep Elgueta — 2004
• A quantum analogue of the Grothendieck–Teichmüller groupKarl-Georg Schlesinger — 2001
• Morphisms between categorified spin networksMatt Hogancamp — 2012
• Higher Dimensional Algebra: I. Braided Monoidal 2-CategoriesJohn C. Baez, Martin Neuchl — 1995
• Higher gauge theory I: 2-BundlesToby Bartels — 2004
• Remarks on Quantum Physics and Noncommutative GeometryLucian M. Ionescu — 2000
• Hopfological algebra and categorification at a root of unity: The first stepsMikhail Khovanov — 2005
• Half-quantum groups at roots of unity, path algebras and representation typeClaude Cibils — 1997
• Dualizable tensor categoriesChristopher L. Douglas, Christopher Schommer‐Pries, Noah Snyder — 2013
• Rota-Baxter CategoriesEdmundo Castillo, Rafael Díaz — 2007
• Higher Lie and Leibniz algebrasDavid Khudaverdyan — 2013

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