Finite Quantum Groupoids and Their Applications

By D. Nikshych, L. Vainerman. 2000

181 citations recorded by the source corpus.

We give a survey of the theory of finite quantum groupoids (weak Hopf algebras), including foundations of the theory and applications to finite depth subfactors, dynamical deformations of quantum groups, and invariants of knots and 3-manifolds.

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

View Paper: https://www.semanticscholar.org/paper/c808a0724b0480cd149163a3c9a6e03ce99284bd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. D. Nikshych
2. V. Ostrik
3. G. Bòhm
4. Zeph Landau
5. Bijan Davvaz
6. V. Leoreanu
7. D. Venku Naidu
8. Michael Mueger

In Geometry and Topology

1. D. Nikshych
2. V. Ostrik
3. G. Bòhm
4. Zeph Landau
5. Bijan Davvaz
6. V. Leoreanu
7. D. Venku Naidu
8. Michael Mueger

In Mathematical Physics

1. D. Nikshych
2. V. Ostrik
3. G. Bòhm
4. Zeph Landau
5. D. Venku Naidu
6. Michael Mueger
7. Liang Kong
8. Pavel Etingof

Citations in the corpus

• Module categories, weak Hopf algebras and modular invariants (2001, background): “he G−action has a natural structure of a fiber functor. (iii) It is well known that the category of representations of a bialgebra is a monoidal category. More generally, let Hbe a weak bialgebra, see [34, 28]. Then the category Rep(H) of H−modules is a monoidal category. (iv) Let A be a semisimple a”
• Binary Relations on Ternary Semihypergroups (2010, background): “For example, in the theory of automata [15] are used n-ary systems satisfying some associative law, some others n-ary systems are applied in the theory of quantum groups [25] and combinatorics [31].”
• On the Structure of Weak Hopf Algebras (2001, background): “Q A ] 1 J un 2”
• Hopf Algebroids (2008, methodology): “In Poisson geometry, solutions of the dynamical Yang-Baxter equation correspond to dynamical quantum groups, which are not Hopf algebras [31], [53], [46], [75], [30], [42].”
• Weak Hopf algebras and quantum groupoids (2002, unknown): “Weak Hopf algebras were defined by Böhm and Szlachányi [2], see also the recent survey [14] by Nikshych and Vainerman and the literature cited there.”
• Exchange Relation Planar Algebras (2002, background): “(Also see the survey [ NiVa ] and the references therein for the non irreducible case.) Here we examine depth 2 irreducible subfactors from a planar algebra point of view.”