Hopfological algebra and categorification at a root of unity: the first steps

Details Hopfological algebra and categorification at a root of unity: the first steps Hopfological algebra and categorification at a root of unity: the first steps

2005-09-04

arxiv.org/abs/math/0509083v2

Mathematics

Quantum Algebra

30 pages, latex, this version contains very minor corrections

Scientific paper

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.

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