Noninvolutory Hopf algebras and \(3\)-manifold invariants

DOI10.1215/S0012-7094-96-08403-3zbMath0949.57003arXivq-alg/9712047MaRDI QIDQ1922420

Greg Kuperberg

Publication date: 31 October 1996

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9712047

zbMATH Keywords

quantum invariantsTQFTReshetikhin-Turaev invariantstopological quantum field theory

Mathematics Subject Classification ID

Related Items (26)

HOPF ALGEBRAS AND INVARIANTS OF COMBED AND FRAMED 3–MANIFOLDS ⋮ HOPF ALGEBRAS AND INVARIANTS OF COMBED AND FRAMED 3–MANIFOLDS ⋮ Integrals, quantum Galois extensions, and the affineness criterion for quantum Yetter-Drinfel'd modules ⋮ \(|Z_{Kup}|=|Z_{Henn}|^{2}\) for lens spaces ⋮ Knots on a torus: A model of the elementary particles ⋮ Boundary and domain wall theories of 2d generalized quantum double model ⋮ State sum invariants of three manifolds from spherical multi-fusion categories ⋮ An approach to categorification of some small quantum groups. II. ⋮ 4-manifold invariants from Hopf algebras ⋮ About homotopy classes of non-singular vector fields on the three-sphere ⋮ Classification of framed links in 3-manifolds ⋮ A modular functor from state sums for finite tensor categories and their bimodules ⋮ Note on infinite iterated crossed products of Hopf algebras and the Drinfeld double. ⋮ Extended graphical calculus for categorified quantum sl(2) ⋮ THREE-DIMENSIONAL 2-FRAMED TQFTS AND SURGERY ⋮ On two invariants of three manifolds from Hopf algebras ⋮ Generalized Kuperberg invariants of 3-manifolds ⋮ COHOMOLOGY OF FROBENIUS ALGEBRAS AND THE YANG-BAXTER EQUATION ⋮ Dualizable tensor categories ⋮ Kuperberg and Turaev-Viro invariants in unimodular categories ⋮ HOMOLOGY 3-SPHERES IN CODIMENSION THREE ⋮ Twisting Kuperberg invariants via Fox calculus and Reidemeister torsion ⋮ Tight contact structures and Anosov flows ⋮ Kuperberg invariants for balanced sutured 3-manifolds ⋮ Invariants of spin three-manifolds from Chern-Simons theory and finite-dimensional Hopf algebras ⋮ Hopfological algebra

Cites Work

• Unnamed Item
• Unnamed Item
• Topological gauge theories and group cohomology
• Finite dimensional cosemisimple Hopf algebras in characteristic 0 are semisimple
• Spherical categories
• The trace function and Hopf algebras
• Ribbon graphs and their invariants derived from quantum groups
• Invariants of 3-manifolds via link polynomials and quantum groups
• STRUCTURE OF TOPOLOGICAL LATTICE FIELD THEORIES IN THREE DIMENSIONS
• QUANTUM INVARIANTS OF 3-MANIFOLDS ASSOCIATED WITH CLASSICAL SIMPLE LIE ALGEBRAS
• INVOLUTORY HOPF ALGEBRAS AND 3-MANIFOLD INVARIANTS
• Canonical Bases Arising from Quantized Enveloping Algebras
• The Order of the Antipode of a Finite Dimensional Hopf Algebra is Finite
• THE QUANTUM G₂ LINK INVARIANT
• Invariants of piecewise-linear 3-manifolds
• INVARIANTS OF 3-MANIFOLDS DERIVED FROM FINITE DIMENSIONAL HOPF ALGEBRAS

This page was built for publication: Noninvolutory Hopf algebras and \(3\)-manifold invariants