Invariants of knots and 3-manifolds from quantum groupoids

By D. Nikshych, Vladimir Turaev, L. Vainerman. 2000

101 citations recorded by the source corpus.

Abstract We use the categories of representations of finite-dimensional quantum groupoids (weak Hopf algebras) to construct ribbon and modular categories that give rise to invariants of knots and 3-manifolds.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b2f44700b18e42d280a0ccd16b5b9da4df94113e

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

An analogue of Radford's S4 formula for finite tensor categories (2004, methodology): “This notion was extended to weak Hopf algebras in [ NTV ] and to quasi-Hopf algebras in [BT].”
Hopf Algebroids (2008, unknown): “Alternative notions 40 Acknowledgement 42 References 42”
On fusion categories (2002, unknown): “vely, As) is generated by the right (respectively, left) tensor factors of ∆(1) in the shortest possible presentation of ∆(1) in A⊗kA. The category Rep(A) of left A-modules is a rigid tensor category [NTV]. The tensor product of two A-modules Vand Wis V⊗At Wwith the A-module structure deﬁned via ∆. ”
Problems on invariants of knots and 3-manifolds (2004, background): “Some other TQFT’s might be obtained from quantum groupoids [314].”
On the Structure of Modular Categories (2002, result): “Thus the proof of the main theorem of [29] could also be deduced from the results of [ 31 ] with some additional effort.”