Hopfological algebra and categorification at a root of unity: The first steps
By Mikhail Khovanov. 2005
77 citations recorded by the source corpus.
Any finite-dimensional Hopf algebra H is Frobenius and the stable category of H-modules is triangulated monoidal. To H-comodule algebras we assign triangulated module-categories over the stable category of H-modules. These module-categories are generalizations of homotopy and derived categories of modules over a differential graded algebra. We expect that, for suitable H, our construction could be a starting point in the program of categorifying quantum invariants of 3-manifolds.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d94b3f3c7d642adac2effe0056278f18da6bc12c
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In Discrete Mathematics and Combinatorics
- You Qi
- Mikhail Khovanov
- S. Wehrli
- S. Morrison
- Jacob Rasmussen
- Sergei Gukov
- I. Cherednik
- Vyacheslav Krushkal
In Geometry and Topology
- You Qi
- Mikhail Khovanov
- Aaron D. Lauda
- David E. V. Rose
- Marko Stosic
- C. Stroppel
- Hoel Queffelec
- Jacob Rasmussen
In Mathematical Physics
- You Qi
- Mikhail Khovanov
- Aaron D. Lauda
- David E. V. Rose
- Marko Stosic
- C. Stroppel
- Hoel Queffelec
- Jacob Rasmussen
Citations in the corpus
- An approach to categorification of some small quantum groups II (2012, background): “Several years ago one of us suggested [18] to study module-categories over H -mod for suitable nitedimensional Hopf algebras H .”
- Hopfological algebra (2012, methodology): “We develop some basic homological theory of hopfological algebra as defined by Khovanov [Hopfological algebra and categorification at a root of unity: the first steps, Preprint (2006), arXiv:math/0509083v2].”