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

2005/09/04 by Mikhail Khovanov, Khovanov, Mikhail · 5 citations
Mathematics · #18G60 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:18G60

paper · pdf · doi:10.48550/arxiv.math/0509083

30 pages, latex, this version contains very minor corrections

openalex publication_date 2005/09/04 · arxiv created 2006/03/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• A local \mathfrakgl_1|1-action on odd Khovanov homology
• Quantum invariants of 3-manifolds and links: a review
• A supergroup series for knot complements
• Cotorsion pairs in Hopfological algebra
• A Prehistory of n-Categorical Physics

Related

• The Hopf category of Frobenius algebras
• Cotorsion pairs in Hopfological algebra
• Hopfological algebra for infinite dimensional Hopf algebras
• Frobenius algebras of corepresentations: gradings
• Module categories over pointed Hopf algebras