scientific article; zbMATH DE number 591017

zbMath0811.17014MaRDI QIDQ4296319

Alfons Van Daele, S. van Keer

Publication date: 12 July 1994

Full work available at URL: http://www.numdam.org/item?id=CM_1994__91_2_201_0

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zbMATH Keywords

Yang-Baxter equationquantum doublePentagon equationfinite-dimensional *-Hopf algebra

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) (46L99) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50)

Related Items (26)

Invariance under twisting for crossed products ⋮ Generalized twistors of nonlocal vertex algebras ⋮ The Drinfel'd double versus the Heisenberg double for an algebraic quantum group. ⋮ Artin-Schelter regularity of twisted tensor products ⋮ More examples of invariance under twisting ⋮ On quasi-Hopf smash products and twisted tensor products of quasialgebras. ⋮ Twistors for modules over algebras ⋮ Twistors of nonlocal vertex algebras ⋮ Nakayama automorphisms of twisted tensor products ⋮ Iterated twisted tensor products of nonlocal vertex algebras ⋮ General twisting of algebras. ⋮ Non commutative truncated polynomial extensions. ⋮ Twisted tensor products of nonlocal vertex algebras ⋮ Triangular \(C^{\ast}\)-bialgebra defined as the direct sum of matrix algebras ⋮ On the classification of twisting maps between \(K^n\) and \(K^m\). ⋮ Twisted tensor product of multiplier Hopf (*-)algebras. ⋮ General twisting of ϕ1-coordinated modules of nonlocal vertex algebras ⋮ Twisted algebras and Rota–Baxter type operators ⋮ Hom-L-R-smash products, Hom-diagonal crossed products and the Drinfeld double of a Hom-Hopf algebra. ⋮ Twisted tensor products of K³ with K³ ⋮ Module twistors for modules of nonlocal vertex algebras ⋮ A Heisenberg double addition to the logarithmic Kazhdan-Lusztig duality. ⋮ The pentagon relation and incidence geometry ⋮ Twisted tensor products of \(K^n\) with \(K^m\) ⋮ Twisted tensor products of \(\phi\)-coordinated modules for nonlocal vertex algebras ⋮ Cohomological properties of the quantum shuffle product and application to the construction of quasi-Hopf algebras

Cites Work

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• Physics for algebraists: Non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction
• Quantum deformation of Lorentz group
• Compact matrix pseudogroups
• Unbounded elements affiliated with \(C^*\)-algebras and non-compact quantum groups
• Hopf-von Neumann algebra bicrossproducts, Kac algebra bicrossproducts, and the classical Yang-Baxter equations
• Solutions of the braid equation related to a Hopf algebra
• More examples of bicrossproduct and double cross product Hopf algebras
• Unitaires multiplicatifs et dualité pour les produits croisés de $\mathrm{C}^*$-algèbres
• INTRODUCTION TO THE YANG-BAXTER EQUATION
• Matched pairs of groups and bismash products of hopf algebras
• Dual Pairs of Hopf *-Algebras

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